Giving chickens heat is more for our peace of mind, than it is for the chickens. They will do fine without heat.
With that said, I choose to go with my peace of mind, for the most part.
I have 2 coops, a larger one and a smaller ones. I keep my younger birds in the larger coop, and I do extended lighting in that coop, giving them 14 hours of light. I normally use a 60watt bulb. I will keep the light on 24/7 if it's so cold and blizzardy, wind chills at 10 degrees or lower and they won't go outside at all. When I do this, my water rarely freezes during that time, so I feel comfortable that they are warm enough.
In my smaller coop, I usually house my older birds, with no extended lighting, hoping to give them a rest for the winter. I do have a light in there, however, which I will use when the conditions are as I described above, an they do just fine. I have a couple of leghorns who have large floppy combs and n the past 4 years, I have not even had any frostbitten combs.
It really comes down to our individual preferences, they will do fine without light, or heat.
A word of warning though, about the space heater....2 years ago, we decided to raise our day old chicks outside in the smaller coop, we used a space heater, we had a divider, and there was no chance of a fire starting, however, our electric bill for the first 4 weeks was $150.00, made them very expensive chicks.