If possible, start doing a lot of ground work around cars. Just have one parked, walk him up to it, let him see it, sniff it. Work up to him being okay with walking past it turned on, then once he's 100% okay with them on the ground, start with under saddle work.
When starting training under saddle, if possible have another, more experience horse there with you. This will also help with his fear of cars. Just remember, all training takes time and it can get a little scary. Just be consistent, steady, and don't push him to far.
Patience, steadiness, and confidence will yield the best results and strengthen the bond between horse and rider.
Good luck and congrats on the new horse!
Wait! I'll fix it....