It works in saved games. It takes time, randomly between one hour up to 1 month for some trees to update.
The game starts at spring, so it will take 6 months to see anything, as there is no content for summer, just autumn and winter. (warmun is autumn, so you should see some changes in the following days)
This mod is very underwhelming. Only those objects in the first screenshot can actually appear, everything else will stay the same in all seasons. For example, only small oaks have winter variation.