Awww- you should try it! LOL, here comes the peer pressure: "It's really fun! And not as dangerous as you think!" (which usually means friends are trying to get you to do something you shouldn't do, haha)Dressage. No way! I’m far to chicken for cross-country
But seriously, if Hudson is obedient enough in his Dressage tests to take 7th out of 30, I bet you and he could clean up the prizes in Eventing at the lower levels, like 70-80cm (no higher than the trot poles or cross rails you've probably already trained with) if it's something that seems fun to you.
Eventing at the low levels is all about getting a good Dressage score, and then going clear over smallish jumps that may look alarming but aren't really very hard if you and Hudson can do basic lengthening and shortening, and he listens to what you want in terms of impulsion. That picture you posted looks like he could do it, and be a lot of fun!
Just offering a suggestion, because Eventing and cross-country is in reality, all about confirming that a horse's Dressage training is solid enough to translate to different types of terrain, which yours seems like it is.
Too many lower-level Eventers (including me, back in the day) concentrate on the fun parts of jumping and just give lip-service to Dressage. We go clear in the Cross-Country and show-jumping, but our Dressage score is mediocre, and we get beat by horses who are great at Dressage and only mediocre at jumping, but obedient and trusting of their riders.
Seriously, you should try it! Hudson seems like one of those "can do it all" horses.
But only if it seems like a fun thing you and Hudson might like to try.