I feel like trotting while warming up is the least of the problems with this post. I think the buteing dead lame horses and riding lame horses should be the main concern for you. But to answer the question I always walk trot/jog canter/lope when warming up my horses before and after I get on. It gets them stretched out, prepares them for whatever level of riding I'll be doing and I can see if they are favoring a leg or acting a bit lame.
Show me a horseman who hasn't fallen and I'll show you a man who has never truly ridden.