Well... yes and no. We have a rescue chihuahua beagle mix. To say that he loves to be held is an understatement! He loves to run around too, but his favorite thing on earth is to be carried. And he's not a small guy either...That poor chihuahua - such a silly costume for a little dog with serious attitude.
And it bugs me a bit when people with little dogs insist on holding them all the time (though maybe in this case it was mostly for the pictures). Those dogs do have legs and do like to walk and run. They are not toys.