Hawthorn although quick growing in its initial growth tends to be a rather dense wood when of any size and prone to splitting if not dried very slowly, If the logs are of a significant diameter I would consider at least splitting them down the core, for me personally as I do a lot of simple segmented constructs I would plank it and stack with spacers to dry it, this would allow it to move with minimum risk of splitting.
I've used quite a bit of Hawthorne over the years, Chas is right in saying it is prone to split, but less so than say Holly which can end up with so many internal splits it becomes unusable (if dried in the round that is). But saw Hawthorne in half and it generally dries pretty well and is very stable once dry. Although it isn't as hard, it makes a decent substitute for boxwood, at least as an ornament. I made the white half of a chess set from it, they are still looking good.