My fave winter riding kit is waterproof shorts, socks and windproof gloves.
However, 2 hours isn't very long to be out, I'd not worry too much. It's when you're out all day, or somewhere remote it matters more. Just layer up, you'll be fine.
Cheapest thing that makes a nice difference is some wooly socks I reckon, will help keep your feet warm even when they get wet. I won some mediumweight north face ones once, and they've been ace cos the fit all my shoes, but are actually pretty warm.