I live in Canada, so I know all about cold. I dress very warmly (Sorel boots, snowmobile mitts, balaclava and ski googles) when clearing snow. I'd be careful about engine heat. Besides the potential for smell, etc., there could be a hazard from exhaust depending on how your exhaust pipe is routed. My 2 small Kubotas blow exhaust at wheel height. My big one exhausts straight up.
If cold is a major issue, many auto parts places sell supplemental heaters based on heated coolant. Its probably an easy install.