Hit the guy who keeps beating you in the knees with a baseball bat, and your next race won't be ruined!
Oh... sorry... I thought the thread title was from the Road forum.
I broke a race on a cheap hub when the cone tightened up as I rode. They are pressed into the hub -- a steel race into an alloy body, usually these days. But, as pointed out, you would have to source a new race, and the effort would make buying a new hub much more efficient. Refinishing probably would be a pointless exercise because the hardened surface has been compromised.
A freehub of the size to fit the number of gears your shifter requires would be a good move. Spin-on freewheels are still relatively easy to find and are cheap, but are at the bottom end of the bicycle retail chain (ie, they will always be fitted to cheap bikes).
Freewheel hubs are renowned for breaking or bending axles because of the outboard location of the driveside bearings. I suspect you have been riding around with a bent axle that has caused damage to the race by misalignment of the load on the balls.
You would be wise to get an entire new built wheel to put immediately back on the bike. But read this page at Sheldon Brown's site first before you decide to go with freehub or freewheel:
If you go freehub, you will need a new cassette and likely a spacer if you cannot source a seven-speed freehub wheel.
Gets complicated, doesn't it?