My daughters are 4 and 6, so we've been working on learning time and referring to the hands a lot. So today when I was working with my kids, I paid attention to the words I use.
When I am trying to describe a hand and explain whether it is an hour or minute hand, I use "short" or "long." So I'll say, "remember, this short hand is the hour hand." I think saying "large" or "small" is confusing to little kids in this circumstance, because their language skills aren't quite up to the level of making the distinction between "large" meaning width versus height. The length tends to be more obvious. Also, the book we're using doesn't really draw the hour hand much fatter than the minute hand.
But, anyway, when I'm talking about a hand and I'm not trying to describe it by size in order to establish which hand it is, I just say "hour" or "minute" hand. I'd also say "second" hand for the one that counts the seconds, except that that one isn't covered in this book or at this level, generally.