Well, it's hard to say. Elephants are tricky creatures, and even assuming that mammoths are domesticable (which is not a given - African elephants to all intents and purposes aren't), there would still be a few problems.
- elephants don't make good cavalry anyway. They are big, impressive, noisy and fairly useless, the Maus to the horse's T-34, is you will. Only males are at all aggressive naturally, and being large creatures without natural predators, even they tend to be fairly sanguine about their environment. If you are that big and strong, there really isn't a lot that you have to worry about, I guess.
- mammoths must have been eating machines. A body that big designed for living in low temperature requires huge amounts of food, and plant food doesn't have that many calories. Modern elephants tend to spend much of the day foraging, and even if given high-energy food they need to spend leisurely hours munching it (the same is true for bulls, BTW). So your cavalry will spend half the day or more ambling through the meadows having vegan lunch.
- mammoths were cold-adapted. An animal this big and this well insulated is likely to have overheating issues even in what we would consider relatively mild summers. Homo sapiens civilisation tends to thrive in temperate-to-warm zones. That means unless you either posit a major POD or a very modern timescale (with the appropriate technologies in place), potential mammoth riders will be nomadic groups with very few resources to spare, which means domesticating anything in the least bit impractical or difficult might just be out of the question. Your typican Nentsi family grouping can't devote the same time and dedication to the effort as an Indian kingdom or Mediterranean city state.
- mammoths might just be natural hippies, or completely intractable, or too stupid, or too smart, or too damn ornery. There is no way of knowing, but chances are there will be some problem, because most big animals have domestication issues.
