When the temperature is hovering around freezing, the last thing you want are squishy, squelchy feet. I am deeply skeptical of On Running's claim that their signature sole bubbles cushion your joints in any significant way against hundreds of pounds of your body weight repeatedly hitting frozen asphalt. However, I do very much like these shoes, which are waterproof (the membrane is recycled). They feel stiff and supportive in mud and have a protective rubber rand around the outside of the shoe. The big lug soles offer lots of traction, but the shoes themselves are insanely light—only 17.6 ounces for the pair. Also, the laces never come undone! 

My other longtime favorites are the Altra Lone Peaks ($170). However, if you don't want to go straight to a trail shoe just yet, you can always try Yaktrax ($35) and waterproof socks ($37) with your regular running running shoes first.