As a Wrestling Coach for over 30 years and also coaching Football for most of that time, I have always encouraged wrestlers to participate in Football or at least another sport each season. If we specialize in our sport we will have a hard time winning the good football player over to even try wrestling. I recruited many wrestlers from the Freshman Football teams over the years. Without other wrestlers playing the sport and showing the value of the crossover from football to wrestling, most would just lift in the off season.
As far as injury, that is always a risk. You have it on the Football field, mat, track or even riding around goofing off. I think your chances are even greater outside due to the fact that you are not involved in an orgainized activity with other kids who have good grades and a common goal.
There is no substitute for competition, whether it is Wrestling, Football, Golf, Badminton or even Basketball, learning to compete is always a positive.