I run MXCs almost all the time. I’ve had them work just fine in 40˚ weather on hard tires, as well as 90˚ weather on soft tires.
I would say in general the MXPs won’t hurt you unless you’re on a medium/soft tire or at a regional/national race.
The MXCs will always provide an advantage in terms of tire consistency. If you’re struggling to get the kart to work consistently through a run and it’s dropping off too quickly at the end, that’s the point the MXCs are your optimal wheel.