Other than Yukon, the most recent trainers have had no issues - so you would *probably* be ok in that case. Although also note I'm not affiliated with CH in any way. I'm just a user who plays COTW and has been doing some investigation on my own prerogative trying to get it all figured out for my own benefit as much as others, so my reply is in no way any official statement, just based on my personal experience.
Even after buying Yukon, but without actually going to the reserve, the last two versions of the trainer worked through multiple launches of the game *for me*, but there are no guarantees with how convoluted this update has become.
Honestly if you take good shots, freeze animals isn't even really necessary, the superspeed loss is what hurts the most for me. 100% quick kill shots make sure they don't go far once shot, and hunting near need zones means animals are easy to find once you've zipped around a map and found them.
I just tried this and can confirm it works!
Wierd, but thanks for figuring this out!
Good to know. I'll update the notes in the game to reflect this at some point.