I'd need to know a bit more about your winter hiking conditions and duration. If you're erring on the side of active, I'd suggest a Labrador. If you're doing colder and shorter, something like a Bernesse Mountain Dog would do amazing.
I love running with my Labrador since she can handle heat decently (I don't run with her when it's very hot), she can handle cold better than I can (has had her whiskers and chest get ice covered), and can handle decent distances in comfort (6-10 miles consistently to age 9).
My only real tips for running with any dogs - be considerate of the heat and make sure you have some good water sources for them.
Update (after 2 years): Our Labrador, now 12, has some hip issues so she's limited to running an easy 2 miles. I never considered Western medicines in the past but acupuncture seems to work wonders for her. We also adopted another dog which we believe is a Lab / Catahoula mix and, holy crap, can that dog run. I have never heard of Catahoula's before but she has no problems keeping up on 15-mile mountain bike rides. My trail runs don't tire her out unless I'm doing 10+ miles, which means she's probably doing 2x that. I'm glad to see them on the list but wouldn't have put them under long slow runs!
As far as running, this article on Runners World should answer;
Ref: The Best Types of Dogs for Runners