Well, given that they wore much heavier armor when jousting than fighting, and used blunted weapons . . . I'd say so.
I think horses wore pretty heavy armor -- a good warhorse was quite valuable, after all.
I've never heard that they wore different armour for jousting, that would certainly be quiet an extra expense on top of everything else. Certainly during the earliest jousting period, about 1070 plate armour wasn't used at all. Full plate armour wouldn't have been universal until about 1400 or so.
The only references I can find for "Jousting" armour is from the 15th and 16th century. By this stage the heavy cavalry tactics on which jousting was based had become obsolete, and Jousting had transformed into a sport with no military connection. As such its training aspect was no longer important, so heavy armor that restricted movement much more then was suitable for the battlefield could be used. Even during this period there was a lighter form of jousting without such excessive armour.
In terms of horse two types were used, the medium-weight horses bred and trained for agility and stamina known as warmblood Chargers, and the Heavy coldblood destriers. The heavy horses were actually slower but at twice the weight of a regular riding horse enabled a much greater impact force.
In terms of speed it would seem they used the Ambling pace for jousting, which is slower then a canter. This allowed the stability needed for aiming.
