Turning a road bike into a cyclocross bike?

I have a decently nice ($1500 range) road bike, but now that winter is approaching, I'm thinking of doing some cyclocross races, just for fun. Do I need to buy a completely new bike specifically for cyclocross or can I put cyclocross tires on my road bike? Also, will a mountain bike work for cyclocross? ... show more I have a decently nice ($1500 range) road bike, but now that winter is approaching, I'm thinking of doing some cyclocross races, just for fun. Do I need to buy a completely new bike specifically for cyclocross or can I put cyclocross tires on my road bike? Also, will a mountain bike work for cyclocross? I'm on a bit of a budget and would like to do this as cheaply as possible, as I'll never be overly competitive in cyclocross--it's just for fun during the winter. Thanks!
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