In all my experience, what you said there really is the key 9/10 times. Even in our last event, where I got 6" of snow on the ground, we struggled like mad to accumulate through about 4:00pm (maybe 1.5" by then) as our surface temp sat at 33F up until that point. I know I was pounding on ptype can be snow at 40F, and it can and my thoughts on ptype worked out just fine with the last event, but accumulation is a different thing. Unless you are getting moderate to heavy snow, it really is difficult to accumulate efficiently above 32F. It'll come in bits and spurts if precip rate increases, but then it melts.
Conversely, even if ground temps are above 40F and the surface temp falls into the 20s, it doesn't take long to start accumulating that way. If I had to choose between a prolonged cold snap with frozen ground and on event day the temps are 32-33F or a prolonged warm spell with ground temps in the mid to upper 40s but on event day surface temps fall into the low to mid 20s I'd choose the later option all other things being equal every time.