The river in the savanna will snow even in the summer after toggle option "shouldSnowyBiomesMeltInSummer" to "false".

Is river incorrectly considered as a snowy biome?

(The snowflakes on the bottom of the screen)

(Current season is summer)

Hmm... the river biome is not considered a snowy biome. So, it is strange you are getting this behavior. Do you have a mod that changes the biomes generated? What is your entire mod list? What does the rest of your config look like? Are you on a single player world? Does your F3 screen show the current biome you are in as well as how many days into the world you are? Did this only start happening with the recent beta release of Fabric Seasons? And does this actually produce and sustain ice?

I may find where the problem is.
The river snow effect out of the winter is just a visual effect, it will not produce ice out of the winter.

For some reason, the client will not update the river season immediately when playing on the server. So you will see the river is snowing even the winter already passed.
It takes time to update to the correct river season. After client updated, river will rain instead of snow.

(but other biomes' season will update on the client as soon as they can)

Hmm... the river biome is not considered a snowy biome. So, it is strange you are getting this behavior. Do you have a mod that changes the biomes generated? What is your entire mod list? What does the rest of your config look like? Are you on a single player world? Does your F3 screen show the current biome you are in as well as how many days into the world you are? Did this only start happening with the recent beta release of Fabric Seasons? And does this actually produce and sustain ice?

Mod list:

Config:
{
"seasonLength": {
"springLength": 1824000,
"summerLength": 2568000,
"fallLength": 1824000,
"winterLength": 2544000
},
"seasonLock": {
"isSeasonLocked": false,
"lockedSeason": "SPRING"
},
"dimensionAllowlist": [
"minecraft:overworld"
],
"doTemperatureChanges": true,
"shouldSnowReplaceVegetation": true,
"shouldSnowyBiomesMeltInSummer": false,
"shouldIceNearWaterMelt": false,
"shouldIceBreakSugarCane": false,
"biomeDenylist": [
"terralith:glacial_chasm",
"minecraft:frozen_ocean",
"minecraft:deep_frozen_ocean",
"minecraft:cold_ocean",
"minecraft:deep_cold_ocean",
"minecraft:ocean",
"minecraft:deep_ocean",
"minecraft:lukewarm_ocean",
"minecraft:deep_lukewarm_ocean",
"minecraft:warm_ocean"
],
"biomeForceSnowInWinterList": [
"minecraft:plains",
"minecraft:sunflower_plains",
"minecraft:stony_peaks"
],
"isSeasonTiedWithSystemTime": false,
"isInNorthHemisphere": true,
"isFallAndSpringReversed": false,
"isSeasonMessingCrops": true,
"isSeasonMessingBonemeal": false,
"doCropsGrowsNormallyUnderground": false,
"doAnimalsBreedInWinter": true,
"notifyCompat": true,
"debugCommandEnabled": false
}

Playing Online

Biome:

I'm using the latest version 2.4.1-BETA

It produce ice

And melt in the spring

As you can see in the background, the river still snow in the summer

I suggest there should be an improvement: The river near a hot biome should not snow in any season.

A snowing savanna/desert river (even in the winter) really looks weird.