First, let me define rhythm and tempo. I want to do this because lots of dressage riders use those terms interchangeably and they don't mean the same thing.
Rhythm - Regularity of the rhythm refers to the even spacing between each step in a stride of walk, trot or canter. Regular rhythm is a priority for all work--whether or not you're riding a pure dressage horse. Movements and exercises should never be done at the expense of rhythm. Rhythm should always stay the same. Tempo or speed, however, is a different matter.
Tempo -- which is the rate of repetition of the rhythm -- can be adjusted, depending on what your horse needs. Think of rhythm and tempo this way: A waltz is always done in 3/4 time. That is the rhythm of a waltz. But a waltz can be played faster or slower. In other words, the tempo can vary.
When should you ride at a tempo that's different from the one your horse chooses? Let's take an overly fresh horse as an example. You start your warm-up, and this horse is so excited that he picks up a trot that is much too quick. The longer you let him go at this clip, the more his tension builds. Left alone, he probably isn't going to slow down. He's like an overtired child who is so wound up that he can't quiet his mind or his body. He needs you to help him calm down by asking him to trot at a much slower tempo than that of his normal working trot.
Slow the tempo by asking for a transition to the walk (or even the halt!), Then, just as he's about to step into the walk, don't finish the transition. Instead, allow him to jog forward very slowly. Think about riding "halfway to walk", and then jog forward slowly. If he accelerates after a few strides, repeat the incomplete downward transition until he understands and is willing to stay in the slower trot.
Ride him in this lazy tempo -- the opposite of what he wants to do -- until he relaxes. Once you feel him relax, gradually allow the tempo to become more normal.
On the other hand, let's say you have a horse that tends to get too slow and labored in his tempo. For example, his canter becomes 4-beat because the tempo is too slow. Quicken his tempo by doing a few strides of a lengthening. Feel how your seat moves faster during the lengthening. Then when you shorten the strides, keep the same quick tempo by moving your seat "as if" you're still lengthening.
So whether or not you're riding a dressage horse, always work in a regular rhythm and a tempo that allows your horse to be in good balance.
A Happy Horse