Looks like it wont work on a server. Heres the relevant bit of the log:
[29Apr2021 15:49:59.740] [main/FATAL] [net.minecraftforge.fml.ModLoader/CORE]: Failed to initialize mod containers
net.minecraftforge.fml.ModLoadingException: Horse Combat Controls has class loading errors
§7java.lang.ExceptionInInitializerError: null
at net.minecraftforge.fml.javafmlmod.FMLModContainer.(FMLModContainer.java:67) ~[?:36.1]
at sun.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method) ~[?:1.8.0_161]
at sun.reflect.NativeConstructorAccessorImpl.newInstance(Unknown Source) ~[?:1.8.0_161]
at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(Unknown Source) ~[?:1.8.0_161]
at java.lang.reflect.Constructor.newInstance(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.javafmlmod.FMLJavaModLanguageProvider$FMLModTarget.loadMod(FMLJavaModLanguageProvider.java:76) ~[?:36.1]
at net.minecraftforge.fml.ModLoader.buildModContainerFromTOML(ModLoader.java:296) ~[?:?]
at net.minecraftforge.fml.ModLoader.lambda$buildMods$29(ModLoader.java:275) ~[?:?]
at java.util.stream.ReferencePipeline$3$1.accept(Unknown Source) ~[?:1.8.0_161]
at java.util.HashMap$EntrySpliterator.forEachRemaining(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.copyInto(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.wrapAndCopyInto(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.ReduceOps$ReduceOp.evaluateSequential(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.evaluate(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.ReferencePipeline.collect(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.ModLoader.buildMods(ModLoader.java:277) ~[?:?]
at net.minecraftforge.fml.ModLoader.lambda$gatherAndInitializeMods$11(ModLoader.java:177) ~[?:?]
at java.util.stream.ReferencePipeline$3$1.accept(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.ReferencePipeline$3$1.accept(Unknown Source) ~[?:1.8.0_161]
at java.util.ArrayList$ArrayListSpliterator.forEachRemaining(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.copyInto(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.wrapAndCopyInto(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.ReduceOps$ReduceOp.evaluateSequential(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.AbstractPipeline.evaluate(Unknown Source) ~[?:1.8.0_161]
at java.util.stream.ReferencePipeline.collect(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.ModLoader.gatherAndInitializeMods(ModLoader.java:179) ~[?:?]
at net.minecraftforge.fml.server.ServerModLoader.load(ServerModLoader.java:44) ~[?:?]
at net.minecraft.server.Main.main(Main.java:95) ~[?:?]
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:1.8.0_161]
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_161]
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_161]
at java.lang.reflect.Method.invoke(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.loading.FMLServerLaunchProvider.lambda$launchService$0(FMLServerLaunchProvider.java:51) ~[forge-1.16.4-35.1.0.jar:36.1]
at cpw.mods.modlauncher.LaunchServiceHandlerDecorator.launch(LaunchServiceHandlerDecorator.java:37) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:54) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:72) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.Launcher.run(Launcher.java:82) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.Launcher.main(Launcher.java:66) [modlauncher-8.0.9.jar:?]
at net.minecraftforge.server.ServerMain$Runner.runLauncher(ServerMain.java:63) [forge-1.16.4-35.1.0.jar:?]
at net.minecraftforge.server.ServerMain$Runner.access$100(ServerMain.java:60) [forge-1.16.4-35.1.0.jar:?]
at net.minecraftforge.server.ServerMain.main(ServerMain.java:57) [forge-1.16.4-35.1.0.jar:?]
Caused by: java.lang.ExceptionInInitializerError
at java.lang.Class.forName0(Native Method) ~[?:1.8.0_161]
at java.lang.Class.forName(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.javafmlmod.FMLModContainer.(FMLModContainer.java:61) ~[?:36.1]
... 40 more
Caused by: java.lang.RuntimeException: Attempted to load class net/minecraft/client/settings/KeyBinding for invalid dist DEDICATED_SERVER
at net.minecraftforge.fml.loading.RuntimeDistCleaner.processClassWithFlags(RuntimeDistCleaner.java:71) ~[forge-1.16.4-35.1.0.jar:36.1]
at cpw.mods.modlauncher.LaunchPluginHandler.offerClassNodeToPlugins(LaunchPluginHandler.java:85) ~[modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.ClassTransformer.transform(ClassTransformer.java:120) ~[modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.TransformingClassLoader$DelegatedClassLoader.findClass(TransformingClassLoader.java:265) ~[modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.TransformingClassLoader.loadClass(TransformingClassLoader.java:136) ~[modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.TransformingClassLoader.loadClass(TransformingClassLoader.java:98) ~[modlauncher-8.0.9.jar:?]
at java.lang.ClassLoader.loadClass(Unknown Source) ~[?:1.8.0_161]
at github.pitbox46.horsecombatcontrols.HorseCombatControls.(HorseCombatControls.java:24) ~[?:1.16.5-1.0.0]
at java.lang.Class.forName0(Native Method) ~[?:1.8.0_161]
at java.lang.Class.forName(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.javafmlmod.FMLModContainer.(FMLModContainer.java:61) ~[?:36.1]
... 40 more
[29Apr2021 15:49:59.820] [main/DEBUG] [net.minecraftforge.fml.ForgeI18n/CORE]: Loading I18N data entries: 4978
[29Apr2021 15:49:59.821] [main/DEBUG] [net.minecraftforge.versions.forge.ForgeVersion/CORE]: Forge Version package package net.minecraftforge.versions.forge, Forge, version 36.1 from cpw.mods.modlauncher.TransformingClassLoader@7cd4a4d7
[29Apr2021 15:49:59.821] [main/DEBUG] [net.minecraftforge.versions.forge.ForgeVersion/CORE]: Found Forge version 36.1.0
[29Apr2021 15:49:59.821] [main/DEBUG] [net.minecraftforge.versions.forge.ForgeVersion/CORE]: Found Forge spec 36.1
[29Apr2021 15:49:59.821] [main/DEBUG] [net.minecraftforge.versions.forge.ForgeVersion/CORE]: Found Forge group net.minecraftforge
[29Apr2021 15:49:59.826] [main/INFO] [STDOUT/]: [net.minecraft.crash.CrashReport:func_85057_a:196]: Negative index in crash report handler (16/18)
[29Apr2021 15:49:59.908] [main/FATAL] [net.minecraftforge.fml.server.ServerModLoader/]: Crash report saved to .\crash-reports\crash-2021-04-29_15.49.59-fml.txt
[29Apr2021 15:50:00.075] [main/FATAL] [net.minecraft.server.Main/]: Failed to start the minecraft server
net.minecraftforge.fml.LoadingFailedException: Loading errors encountered: [
Horse Combat Controls has class loading errors
§7java.lang.ExceptionInInitializerError: null
]
at net.minecraftforge.fml.ModLoader.gatherAndInitializeMods(ModLoader.java:184) ~[?:?]
at net.minecraftforge.fml.server.ServerModLoader.load(ServerModLoader.java:44) ~[?:?]
at net.minecraft.server.Main.main(Main.java:95) ~[?:?]
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) ~[?:1.8.0_161]
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_161]
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source) ~[?:1.8.0_161]
at java.lang.reflect.Method.invoke(Unknown Source) ~[?:1.8.0_161]
at net.minecraftforge.fml.loading.FMLServerLaunchProvider.lambda$launchService$0(FMLServerLaunchProvider.java:51) ~[forge-1.16.4-35.1.0.jar:36.1]
at cpw.mods.modlauncher.LaunchServiceHandlerDecorator.launch(LaunchServiceHandlerDecorator.java:37) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:54) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.LaunchServiceHandler.launch(LaunchServiceHandler.java:72) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.Launcher.run(Launcher.java:82) [modlauncher-8.0.9.jar:?]
at cpw.mods.modlauncher.Launcher.main(Launcher.java:66) [modlauncher-8.0.9.jar:?]
at net.minecraftforge.server.ServerMain$Runner.runLauncher(ServerMain.java:63) [forge-1.16.4-35.1.0.jar:?]
at net.minecraftforge.server.ServerMain$Runner.access$100(ServerMain.java:60) [forge-1.16.4-35.1.0.jar:?]
at net.minecraftforge.server.ServerMain.main(ServerMain.java:57) [forge-1.16.4-35.1.0.jar:?]

I am aware of the server issues and am working on a fix. Hopefully a patch will be out for tonight. Sorry about this.

Fixed in latest commit and curseforge release