Congrats on both kinds of riding lessons! It's too bad one can't use the same helmet for both sports, alas. Sounds like a great adventure - are you going to ride (horses) in Spain too?
Longtime equestrian here - one unsolicited tip - if you find yourself getting tense while on a horse's back, remember to breathe, and smile. It goes a long way to dissipating tension for you and your horse.