Get the cool one, that's the most important. You can always make it warmer later. Before I started lessons, I'd ridden in February on an estuary in biting wind and drizzle. Nothing like what you experience, I imagine, but tough enough for us Brits! To keep my head warm, I used a couple of what my family call neck-scarves. They're those tubes of fabric you pull over your head and leave round your neck as a scarf. We have very thin ones, so I pulled one up until the end was vertically around my head, under my chin, and covered my ears, and then I put the hat on. The other one I was wearing, I pulled up to my chin. It worked wonders.
You can tell how safe a hat is by what safety standards it meets. In America you'll be looking at ASTM F1163; here in the UK you want a hat kite-marked to BS EN 1384 or PAS 015:1998. Above and beyond that, you pay extra for things like it being lightweight or having fancy features or looking good.
The most important thing for hat safety, though, is that it fits properly. There should be no areas of greater pressure or you'll get headaches, and it should be snug enough that when you move the hat, the skin of your forehead moves with it. I was always trying hats that were too big until I got properly fitted. Get yours properly fitted if you can. If you want to buy online cos it's cheaper, go into a tack shop first, find the model that fits and find out what size you need, and then go home and order it.
If you believe everything you read, better not read.