I like the hayhut idea but can not justify spending $800 for a plastic playhouse is what it looks like to me.
I see many had them, they did not last long and were discarded for whatever the reasoning.
So much depends on the animal.
Age and health are factors only you know about.
Weather that is soaking to the skin of a animal makes it so much harder for them to stay warm and it is warm that keeps them comfortable in winter.
You might not need a heavy insulated blanket but maybe a waterproof sheet so the animal not be soaked, has a barrier from stinging rains would be a invited asset to the pony.
A windbreak from cold northern winds my horses like..
I live in Florida, so no snow...but my horses do wear t/o sheets for a wind break and to keep their body dry when we get those nasty rain wind-driven soakers or even a all-day mist that chills the animals.
Winter coats take a lot to soak, but once wet they also take forever to dry...keeping them dry is most of the battle of keeping them comfortable.
If the animal is chilled, offer support of a blanket/sheet.
If they shiver they are working very hard to get warm and burning huge amounts of calories doing so...
If they act miserable, they are...
You will also know if they like the protection a blanket/sheet offers by attitude and body language shown...
Know your horses and pony, know their habits and read their body language will tell you what is best for them...it is about them.
You read & hear all kinds of things about blanketing...from experts and us horselovers. I listen to my animals...they tell me all I need to know on this subject of blanketing, yes or no.