.... WELCOME to the forum!!
Your horse is really cute.
I have one looks nearly the same...flea-bitten gray.
Your horse could use a little weight, but more than weight some muscle.
Hay and pasture is fine for a horse to live off of if they don't need anything else, but you need to also offer proper vitamins and minerals daily then.
With your guy needing a bit of weight and to build muscle, if he were mine I would be giving him Senior feed everyday.
Depending upon the brand will determine how much he is fed.
This would allow him to get some extra calories plus those needed vitamins and minerals to put a bigger shine to his coat, a gleam in his beautiful eye and some muscle to his body you are now riding and exercising a few times a week.
A steady personality I bet he is fun to ride.
If he rides "English" I bet he also knows some already about jumping...
So, look for a Senior feed as through processing it is made differently and nutrients are easier absorbed by the horses body to utilize.
Read the bag directions and introduce it slowly as he is not receiving any feed now...
It will take about 10 days for you to see a difference in appearance...take pictures for comparison or weight tape measurements if you want to know exactly how much he is gaining.
Tweak that amount up or down as is needed and desired goals are reached.
I would estimate he should weigh about 1100 pounds with full weight for his size and build.
With the horse able to eat and do well on hay/pasture now it would not be much he would need fed in Sr. feed.
So, enjoy the new boy and have great fun!!!
May you have many days of riding harmony ahead of you.