The cold won’t bother them as you’ll be bedding them on straw, so they’ll have that and each other for warmth. But the thing that will chill them and potentially make them ill is wet, and particularly if their bedding gets wet so they can’t dry off after coming into the ark.
So the gaps would matter if they’d let rain in to wet the straw in what should be the dry end of the ark. But ventilation is important too, so perhaps some kind of flap you can pull down when it’s wet driving rain from the wrong direction, and otherwise leave it gappy for ventilation?
Depending on breed, you probably won’t need any kind of door. The traditional types will make a straw barrier to keep cold draughts out.
It can catch you out how wet their straw will get once they’re wading through cold wet mud to get into the ark, so use spent straw from inside the ark to build up a pad of not quite so wet and sloppy mud in front of the ark, as a doormat, so they’re not quite so wet and muddy on entering. And regular (like at least every couple of days when the weather is very wet) removal of the spent (ie, wetted) straw from inside the ark will help to keep their bed dry. My sow learned to do this herself, so I just used to give her a couple of flaps of straw every other day and she’d clean out the wet stuff and replace it with fresh herself. But they don’t know that when they’re youngsters, and can get pneumonia frighteningly easily even when they seem to have a lovely dry ark - so get into the habit of putting your hand into the bedding every day so you know for sure it’s dry. And with those gaps at the back, check the bed at the rear of the ark too