Pogies, only thing that works for me
I've tried using my heavy climbing mittens with some success but the constant change in speed and activity level means they can go from too cold to too warm in a matter of minutes. Then I start sweating and they get wet. Instead I use a pair of lightweight poogies with very little insulation and use a pair of medium thickness gloves underneath. The poogies cut the wind(and snow) and the gloves provide the insulation.
My normal pogies are a bit more open than others so I can quickly pull out my hands when I crash or need to adjust something, and my thicker ones are more like the normal design with an adjustable cuff
Btw. if you just want something to deal with occasional bad weather, look at Mountain Hardwear climbing gloves with real large cuffs. Best I found!