Of course I'm not fast on dirt, but here's my input. Whether I do it consiously or not, it doesn't feel like I'm coutersteering in the dirt (unless I'm sliding).
Try this. Ride your bike in 4th on pavement. Look left, push left, go left. Try again on with the right. You'll feel it at speed.
Now ride in 5th, again on pavement and pretend you need to do an evasive manuever. Oil slick right in front of you, LOOKOUT! :) Push hard left, lean left, then push hard right, to straighten the bike back up.
You'll feel the effects of countersteering then, and you'll realize you aren't fast enough and don't really do it enough to notice in the dirt.
On the street, I countersteer into every turn and I feel it. Look left, shift weight, push left, go left. You shouldn't be riding hard enough on the street to lose the front or back end, so you hang your weight of the side, it helps you turn; you can do this because you have traction. Again, this is all for higher speeds (20+), not parking lot manuevers.
On the dirt, it feel betters to weight the outside peg because traction can become unavailable at any moment. With your weight OVER (not off) the bike, you dab and keep going.
OK I'll shut up with one more illustraition, MX guys lay the bike down and stay upright (ass to outside of turn). Roadrace guys lay the bike down and their ass is off the seat to the inside. Two different animals altogether.