You haven't explained why being in a desert would increase a creature's health. And seeing as it is an environment, it would affect the entire board. So it should boost both player's creatures, like nightfall.
Compared to other 'environmental' effects, Desert doesn't seem to provide any logic in terms of its mechanic. Suppose you were to play an Arctic Squid in a water-time duo - how would playing Desert (a Time card) actually improve an Arctic Squid's health pool (a Water card)? It makes sense for Time creatures, but for anything else, it might not (especially creatures that wouldn't want to live in a desert per se...).