In our current world, many plants are adapted for freezes and many are not. In the Mediterranean-like climate where I live, we get hard frosts a handful of times in the winter. They are always just for a few hours at night. And the landscape is completely altered after just one.
The easy answer is to say that plants will evolve to handle freezing temperatures. The reality though is more complex. It's not just about survival.
Let's take the example of a fruiting tree like an apple or cherry. Both do great with freezing temperatures and even thrive in climates with heavy winters each year. But one late frost can affect them greatly. A late frost won't kill them, but it will ruin any flower or young fruit they've put out.
A single frost at the wrong time, even for just a couple of hours, will destroy a fruit tree's ability to put out edible fruit for the entire year.
An early frost, before full harvest, can destroy any fruit left on the tree.
Frosts every couple of weeks year-round? Oy. Very few trees could manage that. Oh they'll survive, but they'll have a difficult time reproducing. They'll produce very few viable seeds and the frosts will kill off all or most of any seedlings that come from those seeds.
Seeds only sprout when the ground temperature is warm enough for them. It takes weeks or months after winter for this to happen. If the ground keeps freezing, they may never sprout. Or they'll sprout and die before they can grow enough to establish themselves.
This is true for all flowering plants that produce fruit, not just fruits humans eat. Flowering plants that produce seeds directly will have similar issues.
Flowering plants are quite old and established as such. Sure, there are flowers that can survive frost, even bloom in it, but they're rare. I'm not sure any fruiting plants (whether tropical, temperate, or with 4 traditional seasons) would survive frosts of this frequency. 1000 years of this and very few, if any, will have survived the reproductive process. (Most would be gone in under 10 years.)
For a lifeform to evolve, some of them have to survive.
Okay, how about non-flowering plants? Plants that reproduce via roots (many do but you need some sexual reproduction for species diversity) or spores (moss, ferns) or seeds (conifers).
Some of these should survive and evolve. You still have the issue of frost killing seedlings, but I can see a few making it through regardless.
Characteristics of plants that survive this process:
- Produce tons and tons of seed/spores/etc.
- Grow well in shade, at least when small (why? because spots up against a large object will have microclimates that aren't as affected by the frosts).
- Very root heavy. All plants have extensive roots (more than people often think) but plants that survive this magic will have large and deep root systems. An 8 hour blizzard won't freeze the ground very deep. So deeper roots are more protected.
Characteristics of warmblooded land animals that survive this process:
- Adapted to eat the plants that have survived (or other animals).
- Skin/fur/feathers/hair that is well insulated.
- No molting periods (at least none that are extreme).
- Can go a day without water.
- Keep eggs warm after laying (or lay them underground).
- Care for young after birth.
- Mammals will have very fatty milk.