That would depend on region... and what you mean by hard.

Rain forests such as those found in India, Northern Australia, Soath East Asia would likely be very heavily hit. The rapid cooling will likely be playing havok with their monsoons which are critical for replenishing the water they loose.

Rain forests that can sustain their own rainfall, such as the Amazon Rain Forest, and rainforest built over great untapped aquifiers, such as those around the K2 impact crater could sustain themselves in the face of interrupted rainfall for some time.

All of them will be disrupted by the rapidly changing temperature. Expect the die off of tightly coupled species particularly if those species have some sort of mechanic around temperature, such as migration, seeding, nesting, etc...

Temperate regions rely less on rainfall for maintaining the forest. Their chief issue will be how cold adapted the trees are.

• Regions heavily populated by conifers will probably handle well. Conifers have been through many periods of extended cold.
• Broadleaf evergreens will be hit hard as their leaves are destroyed by frost.
• Broadleaf annuals will survive, though only growing during the "summer" presuming summer months warm sufficiently.

However this is if you take the view that a forest is the expected biome.

What will likely happen is that many forests will transition in grasslands/tundra. Producing a resurgence in C4 plants. This will naturally provide a field day for every C4 herbivorous animal, and the resulting food chain that they bring with them.

Naturally this isn't a terribly nice world for Nut/Fruit eaters...

That would depend on region... and what you mean by hard.

Rain forests such as those found in India, Northern Australia, Soath East Asia would likely be very heavily hit. The rapid cooling will likely be playing havok with their monsoons which are critical for replenishing the water they loose.

Rain forests that can sustain their own rainfall, such as the Amazon Rain Forest, and rainforest built over great untapped aquifiers, such as those around the K2 impact crater could sustain themselves in the face of interrupted rainfall for some time.

All of them will be disrupted by the rapidly changing temperature. Expect the die off of tightly coupled species particularly if those species have some sort of mechanic around temperature, such as migration, seeding, nesting, etc...

Temperate regions rely less on rainfall for maintaining the forest. Their chief issue will be how cold adapted the trees are.

• Regions heavily populated by conifers will probably handle well. Conifers have been through many periods of extended cold.
• Broadleaf evergreens will be hit hard as their leaves are destroyed by frost.
• Broadleaf deciduous will survive, though only growing during the "summer" presuming summer months warm sufficiently.

However this is if you take the view that a forest is the expected biome.

What will likely happen is that many forests will transition in grasslands/tundra. Producing a resurgence in C4 plants. This will naturally provide a field day for every C4 herbivorous animal, and the resulting food chain that they bring with them.

Naturally this isn't a terribly nice world for Nut/Fruit eaters...