MUA is OA.
The trick is that the hood MUA is NEVER equal to or greater than the hood exhaust, it's been awhile since I designed a kitchen, I believe the rule of thumb is that hood MUA is 75-80% of hood exhaust. You end up with an area of negative pressure under the hood which is where your smoke and fumes are located. This negative area will keep smoke and fumes under the hood out of the rest of the kitchen.
To maintain a positive building pressurization you still need to bring enough outside air into the building through your main HVAC system(s) to make up the remaining 20-25% plus enough for toilet exhausts and any other code mandated exhaust in sufficient quantity.
For example assume a small restaurant with one hood and two toilets and 50 seats.
Hood exhausts 5,000 CFM, toilets 200 CFM for a total 5,200 CFM EA.
Outside air requirement is going to be 1,000 CFM (let's keep the math simple here).
You have two options:
1) provide 4,000 CFM unconditioned MUA at the hood, and 1,500+ CFM through your main HVAC units
2) introduce 5,500+ CFM through your main HVAC units.
I hope I don't have to explain what the difference in OA will have on sizing the main HVAC units.
There is no code or guide that prohibits MUA from being heated or cooled.
Not all hoods have or need MUA. A lot of small shops will have a small hood over a grille and run with 1,000 CFM exhaust or less. In these cases there is often no need for MUA as the requisite amount of outside air for the rest of the kitchen is sufficient to keep the place positive while still controlling smoke and fumes.