choosing training arenas

Do I need to choose different training arenas for each of my N1, N2, N3 horses ? Those arenas are all listed as Novice (without numbers) but in the search different arenas show up for N1,N2,N3 horses (different names).
So if I find arena for my N1 horse, can I also train there my other horses which are N2, N3 (they're all the same speciality) or will it affect their training progress?

You can train all your novice horses in the same arena. :)
For example a N1 western horse and a N5 western horse in a novice western arena and so on. 
Hope that makes sense, I´m really tired today. :P

It does, thank you !