I did and still do. It's just a matter of time management.
I did my undergrad at a uni in Massachusetts that had its own stables, which was the most convenient thing, ever, as the barn was all of five minutes away from the dorms. You're taking a lot of classes as an undergrad so you haven't tons of free time to be schlepping all over the place to ride. When I did my master's in Durham (England) she was unfortunately about half an hour away. Then when I moved to Edinburgh, she was about 15-20 minutes away, which wasn't so bad. Now she is 30-45 minutes away and it is a bloody hassle but what can you do? I still make the time.
If you can, unis in more rural areas (so very few places in the UK but loads of them in the States) will make it easier, as the chances of finding a barn near the uni increase exponentially. I remember when I was looking at colleges, thinking this was a priority, purposefully not looking at anything in big cities and especially focusing on the unis which had their own stables. These days I've just had to resign myself to a long commute.