I once tried cycling in a similar amount of snow to that and found:

• I slid in one place and nearly fell off
• My glasses got covered in snow and using your finger as a windscreen wiper is annoying
• My gear mechanism got gummed up so I could only shift gears in one direction (pulling the cable worked, but the spring tension was not enough to retract it again)
• My chain got covered in snow which washed off the lubricant and in salt-water from road salt which rusted it quickly

so since then I have not tried again. Also we don't get much snow so there are few opportunities...