Parched earth might offer the danger of wide cracks in the surface that (because they are solid at the edges) if a player's foot/heel got caught or twisted, but the main accepted difference is frozen ground has no give in it where it's full of frozen water, making it like concrete. Hard dry ground is at least likely to have more than a little 'give' in it when players fall on it.
I'm remembering a slide tackle graze I picked up in '76 on hard ground, went from my left shoulder (I didn't have moobs then as a 17 year old!) via my hip bone to my left thigh and knee. It wept for 2-3 weeks and stung like a demon in the bath...........stayed on my feet till the end of the season, and ALWAYS tucked my shirt in properly. Grazed boob, not good!!