Not all vents need to be 2 inches. That was probably not your question. It is possible that your 3 inch line is not technically enough to accept all of the vents. I am not knowledgeable as to what total vents you are allowed merge into a 3 inch line. I just happened to have some knowledge of the sewage pit requirement. I think the reason that cold areas often require bigger pipe through the roof is to allow for accumulation of some ice and snow that reduces the effective diameter.
You might want to talk with the building department or inspector, since some rules can vary from place to place.
Air is air... and a vent is a vent.... 1/1/2 will work fine ....2 is better.....
In our state all you need to go out the roof is one 1 1/2 vent for a complete home 5 bathrooms
it works ok.... I would prefer more vents but it seems to function fine...
Different areas require more venting but I have seen homes plumbed with the minimal
and they work fine even in the polar vortex last year....
if you are doing some commando job in your basement I have seen homes with only a anto air vent on
the sewage pit in the past... and that is the bare minimum you can do....