Some bunnies do seem to just shed constantly. It’s not worrying in itself, but you need to make sure hes not ingesting too much fur, which could be causing gas pains and mini stomach blockages. Especially indoor rabbits don’t necessarily moult with the correct seasons.

You can definitely open the door and see if he wants to go out. He won’t get sick from a few minutes outside as long as he’s warm and dry afterwards, but he might not want to go out. You could put a little mat or something down so he has somewhere warm to sit if wants. Or you could fill a little tray with snow and bring it in for them to dig in if they want

It sounds like their diet is great

My boy Bombur is constantly shedding, and there’s nothing wrong with him in that department. He just sheds. You get a week or two break, but then he starts all over again. It is quite frustrating though xD A good trick if one of them is ingesting too much fur is to go over them with a lint roller. S&L taught me that trick a while ago and I’ve been using it ever since!

Shedding varies from bunny to bunny. Corrie sheds all the freaking time, but Albrecht only sheds in the summer.
If you notice his droppings are strung together by fur, he is ingesting way to much and needs to be groomed more frequently, If not, its all good.
Since rabbits grow all that fur, 0 C isn’t cold at all. Rabbits prefer cooler temperatures to warm. Mine are the happiest around 40 or 50 F. The only concern with snow is their feet getting cold and wet, and you can solve that by putting a piece of cardboard with a towel or blanket over it in the run with them to sit on.