Thinking back to when I was a kid.....
Summer stuff on the grass was a real pain for me, I overheated very quickly which for me resulted in a banging headache, add that to the hayfever and what the useless docs later found out was asthma and it was no fun at all, PE teachers used to tell me I was unfit all the time and it was very depressing! It was all so bad because of THEIR lack of education, they chose not to find out if my skin condition could be the cause of my so called 'unfitness'.
Winter had its own problems with overheating and extra sore skin, but... I did have one magic moment at school, we went out one winter when I was 14 for the weekly cross-country run, freezing cold day and as usual I was at the back, this was to be a two hour run but about 20 mins into it the heavens opened and it poured down like I had never seen it before, the rain was an absolute godsend for me, within twenty mins I was at the head of the field and won the race by over ten minutes from the second place :-)) That day I proved to the whole school I was not unfit, they still didnt understand my condition but it gave me the biggest smile for weeks, at 38 I still go for a run every now and then.......but only if its raining!
Basically what I'm saying is make sure that ALL the teachers, friends parents, friends themselves, and you as the parents know what other symptoms that cant be outwardly seen can arrise, no doubt they wont be the same for everyone but so long as everyone is aware of the limits and symptoms there's no reason why your little one cant enjoy a wise variety of sports :-)