Winter

In the driving ones, genuinely different physics - ice reduces grip so braking distances and cornering both change. Elsewhere it's mostly a seasonal theme applied over a normal puzzle or sport.

A sport where you slide a stone across ice toward a target, sweeping ahead of it to control speed and direction. Sweeper Curling is a decent introduction if you have only seen it on television.

Grip, mostly. It's the same bike and the same controls, but ice under the wheels changes braking and take-off timing, so lines that worked on tarmac need adjusting.

Of course. They're available year-round and most are simply good games with a seasonal coat of paint, so nothing about them depends on the time of year.

Yes, all of them run free in your browser with nothing to install and no account needed before you start, whatever the weather is doing outside.