There can be marish mares, and studdy geldings. All depends on the horse. Also keep in mind that not all horses show ‘love’ in the form of allowing hugs and kisses from humans. Some horses, like people, need their space, but will show ‘love’ in other ways.
So, if you need a horse to physically hug and kiss make sure before you buy any horse, make sure that particular horse allows that kind of contact.
My Arab gelding is the first to the gate, comes when called (until the new spring grass is coming up), easy to deal with on the ground, nickers and mumbles when I enter the barn or pasture, and respects your space and wants humans to respect his.....so do not try to hug or kiss him. Despite that, he is one of the most ‘loving’ horses I have had the pleasure of owning.
I think any horse can be taught to let 'their' human hug, kiss and basically invade their space and do it willingly. I start with my babies, they have to allow kisses on their little noses, in the soft fur behind their ears and pets, hugs and touching anywhere I want. At first they remind me of Lucy in the Peanuts cartoons, "AAAUUUUGH Human Germs! Where's the peroxide?" but real soon they associate all that nonsense with scritches in their favorite places and treats.
Older horses may take longer and may never be real willing to allow all that familiarity. Patti loves to have the soft fur behind her ears stroked and kissed, I wouldn't even think of doing it with Boo (for one thing, I can't reach that high), she hasn't come along enough in the "I crave attention" spectrum for either one of us to be comfortable with that. But she does allow and even, dare I say, enjoys it when I put sunscreen on her muzzle. She may not LOVE it, but she has made the connection between sunscreen and not getting blistered and uncomfortable. When I first got her, that was a serious "No Trespassing" area.
For a beginner, especially a beginner with anxiety, I would recommend a horse who will allow you to snuggle up, kiss and touch and just generally be a close proximity pain in their tail.