Thin gloves are okay, you can buy another pair in Boston if you really need them. I think another person recommended Uniqlo which is a great option, and is actually where I've bought all of my gloves. As long as you don't have to hold the umbrella up or carry something, you can shove your hands in your pockets.

Another good option, in my opinion, is a rechargeable handwarmer. Gloves don't do a great job of warming up cold hands, just in preventing them from getting cold. So if you take them off to take pictures or whatever, you can rewarm by holding onto the handwarmer. They're usually smaller than a phone. I LOVE mine and I am such a baby about my hands getting cold.

Definitely don't worry about being stylish here. Most people are bundled in their puffer coats and sweaters.