The old-fashioned idea of greasing the feet to stop the snow balling in the hooves, still stands. Just use any really thick industrial grease – it won’t hurt the hooves short term – just apply it to the sole and inside of the hooves before you ride out.
In colder countries they use special rubber ‘bubble’ pads to help the snow pop out. But there’s not much call for these in the UK as it gets so little snow. Of course, there could be a return of the ‘beast from the east’, so it’s as well to know there are options.
With barefoot horses, you don’t get the issues that you get with shod horses ie the snow freezing onto the metal of the shoe and causing balling in the horses foot - ‘snow stilts’ which are dangerous. So riding a barefoot horse on good ground can also be perfectly safe in the snow.
When considering riding in snow, it’s all about being sensible. Ice is much more dangerous than snow. So be careful if the snow freezes. Otherwise, consider the benefit of a gentle ride on snow against the risk of not riding your horse for a few days and it getting fresher and fresher in the cold weather.
Of course, if you’re lucky enough to have the use of an indoor school, you may never have to go through these dilemmas. Not that we’re jealous or anything.