I didn't have a heart attack. In 2002 I did have a 98% (the Doc said maybe even 99%!) blockage of the Left Anterior Descent (LAD) artery. It presented merely as shortness of breath on a 2 mile walk on a cold February day. I was very lucky, caught it before I was really in trouble. They just put a stent in; there wasn't any damage. I got good advice on getting treatment quickly from a Doctor whose land I hunted. See...there's a reason to be a hunter.
I hunted that Fall and every Fall since. I did lose some weight and get in better shape, knocked my LDL cholesterol number way down, took a statin and a coated aspirin every day.
The only caveat the Docs gave me about hunting was to watch it in extremely cold weather. The heart has to work harder to maintain core temperature and also pump that blood out to the extremities. Filling your lungs with below freezing air doesn't help this; it can decrease your lung capacity = less oxygen to the blood/heart. So for the first couple of years they had me wearing a PolarWrap heat exchanger mask when it was really cold. Looks like they are out of business now though.
https://www.amazon.com/Polarwrap-Exchanger-Model-Mossy-Break-Up/dp/B000JKLBFY
At any rate, I don't use the mask anymore. I DO use a light polyester hood from Cabela's. It's basically a lightweight balaclava that you can stuff in a pocket and keep handy. They say you lose 20% of your body heat through an uncovered head. I personally feel like putting on the hood is like putting on a light sweater. I'm out on a nice chilly Fall day, great day to be afield and the temp drops 10-15 degrees and a wicked wind comes up...out comes the hood. Amazing what the one small change does for my personal warmth. I find it is better than the PolarWrap, it's way more comfortable and unobtrusive and just that layer of material over your mouth warms the air a bit. Not as much as the PolarWrap but sufficient for me. About $15 Cabela's Men's Camoskinz? Hood. There is ALWAYS one in my strap vest.
Other than that, I haven't changed anything. I hunt now like I did before the stent. I do make it a practice to walk with my dogs every possible day. I usually get in 4-5 miles a day at just under 4 mph. I figure if I can do that without discomfort, I can hunt the fields.
OK...maybe I do use a bit more common sense than when I was younger. When I find myself in the rough going, hacking through the cattails or heavy cover, I slow down. When I find myself getting winded and my heart first begins to pound a bit...I stop until I'm rested.
In your case, fresh off the heart attack, you want to take it easy this year and see how you feel as you go. Always go out with someone else. Get the young studs to walk the tough stuff, you take the edge. Don't press; try a couple of short hunts first, don't go at it all day long right off the get-go. Don't be afraid to sit out a day and let your body rest. Watch the below zero breathing.
Lastly, and I don't mean for this to sound stupid, pheasant hunting with dogs is the main reason I am able to put up with the BS the rest of the year provides in ample quantity. If I couldn't do it, I'd be miserable. So, knowing that none of us get out of this alive, I'm going hunting anyway. I had that attitude right after they put the stent in and I still have it 14 years later.
So, do what the Docs say, be in the best walking shape you can manage before you start and then go on a few short hunts and see how it goes.
Good luck and good hunting!