'first past the post'

Actually, here we generally say "first outta the gate" which probably makes more sense since that doesn't imply that the person has won like "first past the post" does.

Nipped at the wire I have never heard. Nipped at/in the bud is quite a common expression meaning it was stopped right at the start or just as it was beginning to form.

As to racing term...in Québec we are notorious for enthusiastically going anywhere that is *not the race track. The one we have is subsidized by the govt and caters to a few hundred people on weekends.