let the horse adapt to the weather bit by bit, so I would skip the blanket for your locale. Horse will grow hair and become used to the colder weather as the days pass. As long as the horse has protection from the wind and plenty of hay to eat, it should be fine. I live near Seattle, and we never blanket ours , which live out 24/7.
The horse putting it's head down; Yeah, you can let it try and see what it is doing. I let my horse put his head down sometimes to sniff poo or what not. But the key is that I LET him do it. He does NOT barge the reins out of my hand. And if he starts to eat, then no more letting the head down. He knows trail snacking is forbidden. I neve let him graze when I am in the saddle.
If a horse I am riding tries to snack along the way, instead of pulling the head up, I put the leg or whip ON! I move him forward, bang! He will whip his head up and leap forward. Next time, all I have to do is threaten to put the whip on and he will leave off trying to eat. But don't play pull up, play move on!