You can use studded tyres in ice and snow. Schwalbe Snow Studs don't have studs in the centre, so are 'better' for tarmac and can be used off road. Run the tyres at 30 PSI and the studs remain in contact with the road, run higher and they don't.
The more 'studs' the more expensive they get. The Snow studs are more of an 'off road' tyre, and you can get tyres that are more road suited. And tyres that are better 'off road'. Snow Studs sit in the middle.
Any MTB tyre works well in deep snow. Studs come in when things get compacted and icy.