I also pasture board.
In previous years, my girl has been out all day and out all night with the option of using a large run-in (one thing to be careful of is, if you're "relying" on the run-in, make sure your horse will have access - ie, not more dominant horses running her off, it's big enough for all the horse in the pasture, etc). She's not pastured with horses so being run off isn't a problem for her.
This year, however, she's starting to show her age a bit more with a variety of health problems that aren't going to improve (Moon Blindness, her internal heating/cooling "system" is getting a bit wacko, etc, she's 27) so she's now stalled on especially hot days and will be stalled overnight during the winter. During the winter, she also wears a ridiculous number of blankets to keep herself warm but it works for her so I guess I'm happy! haha
Anyway, basically, your little girl should be fine out. It'll probably actually be better for her since she is young - more time to really be a horse. You want her to grow up self reliant vs something that can't stand the rain!
The lack of training facilities, that could be a problem. However, she is just a yearling so you could board her at this place until you want to really get into training her, then move to a place with better facilities while she needs them.
I have very little experience with babies but from what I've seen, often they don't require a whole lot. I mean, she's too young to lunge, to young to roundpen, old enough to pony but that doesn't require facilities, old enough to introduce to various obstacles which also doesn't require facilities... Maybe it would work out fine?