There are no special safety issues related to snow and ice.
In general, voltages up to 48V are considered safe for the human body. You can touch both contacts of a 12V battery, even with wet fingers. (Did you never touch the terminals of a 9V battery with your tongue? This hurts a little, but that's all)
A 12V car battery can deliver several 100 Ampere, but therefore, the resistance of the circuit must be low. For example, a resistance of 0.03 Ohm connected to 12V will sink a current of 400A. But the resistance between a finger of the right and a finger of the left hand is in the order of several 100000 Ohm for dry skin and in worst case may be 1000 Ohm for very wet skin. This causes currents of 0.00012A to 0.012A, which is still much smaller that 0.05A, which is considered as the threshold where current starts do be unhealthy. In absolutely worst case, you might feel the current, but usually, you will not.
So, for snow and ice, the rules are the same.
- Start the other car
- Don't short circuit the battery by any piece of metal, because metal has a low resistance. The current flowing can be high enough to melt the metal.
- Pay attention to the polarity. Connect plus to plus and minus to minus (chassis) Doing this wrong results in a short circuit.
- Connect plus first via the positive battery terminals.
- Connect minus from the negative battery terminal of the running vehicle to a solid part of the chassis or better motor block of the other car. (In this order!)
- Try to start the car.
- When it's running, let it run for a minute or two. Then, switch on a high load like rear window heater or air blower. This will avoid voltage spikes which could damage the electronics of the car
- Remove the clamps in reverse order.