I think most people don't wear anything underneath their helmet. There are a couple good reasons for this.
1. The effectiveness of a helmet is predicated on the assumption that it will be directly in contact with your head. Most helmet manufacturers will tell you not to wear anything under your helmet.
2. Helmets are pretty darn warm already. The vents in most helmets won't allow enough airflow to actually make your head cold. If you're wearing Goggles, then your eyes and upper face will be protected, and then you can just get a neck warmer or one of those bandana type things to cover your lower face and neck.