Crops planted outdoors will only be able to grow in whatever season they're for. They'll have to be planted indoors out of season, in a building made of greenhouse glass.

Vanilla crop listings:

Wheat - Summer/Autumn
Carrots - Spring
Potatoes - Spring
Beetroot - Autumn
Melons - Summer
Pumpkins - Autumn

Please give us a config this time to add crops from other mods.

There will be a config file.

Plants inside a forestry greenhouse should be unaffected by this. If the temperature inside the greenhouse is above freezing they should grow normally

I mentioned some of this in Discord already but I feel I can explain my idea more completely here:

The ability to tie crop death to a minimum/maximum biome temperature (which ought to rise higher than the default in summer and drop lower than the default in winter) would allow more dynamic growing seasons for different crops as well as crop death from overheating. It would also work better with custom biomes from OTG, RTG, and other mods with minimal to no further configuring by using a commonly shared vanilla characteristic. It also resolves the potential issue of when one biome's winter is warmer than another's summer but still unable to support crops while the other can.

For example, sugarcane may only be able to grow at a minimum temperature of 0.9 and a maximum of 2.2 (values are totally subjective). So a warmer biome, or at least one with a temperature that stays within the limits for more or all of the seasons, would have a longer or year-round growing season for sugarcane. A biome with a temperature range that is always outside the limits (like Cold Taiga, or a custom biome with a ridiculously high temperature like 5.0) would never be able to support unsheltered sugarcane, no matter the season.

A crop like beetroot may possible only grow between 0.2 and 1.0 (again, the specific values are totally subjective). So a cooler biome would have a longer growing season for beetroot, provided it does not get too cold. But a warmer biome during the summer will get too hot for the beetroot, killing them off.

Wheat may only grow between 0.5 and 1.5, cactus between 1.5 and 2.5, potatoes between 0.2 and 1.2, and so on. Players can decide what min or max temperatures turn their crops into dead crops. Ultimately most farming will still follow the common pattern of growth in the spring/summer and harvest/death in autumn/winter due to the temperatures the crops naturally grow in. However, opting for temperature as the variable rather than current season will maintain the overall effects of seasons while opening up possibilities like extremophile plants and varying growing seasons based on biome and crop type.

@WrongWeekend I agree a system like that would be much more flexible and fun. However may I make a further suggestion if it is decided to go this road:

Give each crop an extra option: perennial = true | false which determines if the crop either dies or reverts back to stage 0.

EDIT: The reasoning behind this is that certain mods distribute their crops using worldgen. So that way you can still get their seeds. Besides, it would be nice to have at least some (selective) crops grow without having to replant each year.