Pressure treated lumber will be okay.
It's not just firewood that is an issue. Any wood that is not sawn and kiln dried (like dimensional construction lumber for ex.) is not permitted. The rules can vary from west to east coast due to different destructive insects and diseases. "Firewood" and "treated lumber" and "wood products" have different definitions. Treated lumber means either commercial kiln drying or chemical treatment. If you had your own mill to make lumber from trees, that would not be allowed. We only ever take manufactured sawn (heat treated) lumber across the border and it is okay here.
CBP info.
here and
here. CBSA info.
here and
here. Because the rules vary from coast to coast and are subject to change, the best thing to do if you are unsure is to contact CBSA or CBP. The last thing you want is to be turned back at the border or have your Nexus revoked.
We got pulled over for a random inspection a few weeks ago entering the US. We had firewood and kindling (kiln dried & sawn lumber) and they went through every single piece. They found a couple of pieces of kindling (from sawn lumber) that had bark on them and we got a stern warning. Funny thing was, we bought the wood at a pallet manufacturer in the US that cuts scrap wood into firewood size pieces and we had also been carrying back and forth across the border for a year or more. The pallet wood could be from outside North America.