Have to say I consider any icing on these trainers to be "severe", you shouldn't be in clouds if there is the slightest chance of icing, but I am a grey-haired pussy now.
I think autumn is probably best, as you've got most stability.
That would be a bad time to learn then, you want to be thrown around in your training, not good if you find yourself shooting your first bumpy IMC approach with 16.1 hours under the hood.