I'm going through a similar experience with my horse, a 7 year old 3/4 tb x han. My horse had a 2000 mile move to a new area and was under weight before he left and lost more weight from the stress of the move.
The area we're in has extremely cold weather (average daily highs of -25 to -40 degrees Celsius) so he has to be kept at a place with a heated arena. However "turnout" is a 10 by 15 pen, and it's frequently too cold for turnout at all.
I started feeding my guy unlimited hay, with 3 times daily feedings of 1.5 lbs oats and 1.5 lbs of a complete pellet with 20% fat. He did well on this for about 2.5 weeks and was gaining weight nicely. Then his temperament changed and he was quite hot and threw a bucking fit that tossed me off and then he nearly flipped over backward on me (a normally dead quiet horse). So I cut his feed down to twice a day feeds as I wanted him to get enough extra calories for weight gain, but not be exploding on me. This worked well for another 3 weeks or so and he has gained weight to a nice ideal weight now and then same thing again, he started to get too hot again. So now I've halved the amount of grain he gets twice a day. We'll see how this works and if he starts to lose condition (I don't think he will) I can also up the grain a little bit more or try to find some better quality hay.
Best of luck with your guy. I hope you get something figured out for him.