Our hay is virtually as you described yours, a good portion alfalfa and the rest is a mix of grass/timothy. We purchase 800lb square bales and when cold hits, our horses are NEVER without food. If they go longer then 2 hours without hay, they will start shivering. They get limited exercise in winter, so they never get "fat" - however, they DO come into spring heavier then when they went into winter which is a good sign of a proper feeding program. I always like putting an extra layer of fat on my horses before winter hits.
However, if your horse comes into the barn or even wears a winter blanket, this heat source isn't quite as crucial. In cold months however, he still shouldn't go very many hours without food. They require almost a constant intake of food to maintain body warmth in the winter months. Unlike in summer months, this food isn't just going to create a massive belly, it's all being used to maintain body heat and keep what fat they DO have.
When cold hits, I definitely think a constant source of food is the best option. Giving that an average bale of hay weights roughly 50lbs (give or take), he shouldn't be able to actually consume an entire bale a day. If you feed him grains/concentrates, I'd just stop that for winter unless you're riding him regularly as his body will run much more efficiently if he's allowed to just fill himself with hay as neccesary. I'd start him off with half a bale in the morning and see how long it takes him to finish it.
We have wood feeders set up by the fence to throw hay into easily so not as much is wasted. We usually cram the feeders as full as we can get them which typically provides our herd of 7 1/2 (LOL, miniature) horses with a couple of days of feed.
What's ironic is that free fed horses actually tend to NOT gorge themselves. Gorging is quite often a symptom of horses that get fed on a schedule - they're so hungry by the time the food comes, they're convinced they need to wolf it all down. Because our herd spends the entire summer grazing with supplemented hay when fall hits, free feeding in winter doesn't cause us any weight problems even WITH our extremely easy keepers. They're accustomed to always having food around, so it's natural for them to simply take as they require. Now that it's chilly and the pasture is sparse, we always keep a bit of hay in the feed bin and yet they're always out grazing down the last bits of yummy grass over alfalfa. They know it's there and they know it's not going anywhere, so they're getting as much grass as they can before snow flies!