looking for honey mushrooms
I'm not sure exactly what type of mushroom you're referring to, but there is a wild mushroom that is sometimes called a honey mushroom (Armillaria mellea, I think). It would be very completely out of season right now - it grows wild in Ontario in late summer and early fall. I don't think they've been cultivated so you might be out of luck. There's another type of mushroom which is sometimes called Ontario Pine Mushroom (Tricholoma Terreum) that is sold at the St. Lawrence market in the fall. I have gone out picking with the "Mushroom Lady" who gathers these things. They're small and greyish - and very delicious. These are also out of season so you'll have to wait until next October.
Most of the "wild" mushrooms that are readily available are really cultivated versions of that mushroom. Oysters, shitakes, portobellos - they're grown in mushroom farms. I think someone is working on a way to cultivate morels, but so far it has not been successful. And I don't think porcinis have been cultivated either, but I do know where you can find them in the fall.