What do those crosses mean?
Usually they stands for indetermined pitch sound, in special mode percussive or spoken/shouted.
In this case they seem pitched.
The instruments are trumpet and sax. For sax it could maybe indicate slapped, but for trumpet?
They're "ghost notes". You play them, but just kind of "swallow" them so while they're there they aren't emphasized in any way.
It makes sense but...
Probably it's easier to do than to explain them. ;)
Thanks
Happy new year, one and all.
I agree with Lawrie's answer, but just in case it isn't obvious: do not slap tongue those x notes if you're on reeds.