I have been in the same situation.
If your seat type requires that a portion of the seat cover must be stapled to the wood/plastic that you are replacing then ensure that staples will penetrate and hold in the plastic. The wood base will hold the staples.
Likely the fasteners that you spoke of were T-bolts. You can see that the two slots on the back of the tunnel one on each side are used to bolt the seat down to the back of the tunnel. Your original wooden board is likely rotten beyond use at those original mounting points. If your snow machine is liquid cooled then there may be a pair of heat exchangers running under the tunnel at these mounting holes.This reduces the area that you would want to be drilling into if you just wanted to reuse the original base/board from the seat. If air cooled then your mounting locations are less limited. T-nuts also work well in the seat mounting base/board. Replacing the seat board/base now will likely mean that this replaced seat base/board may long outlast the snow machine. I know it will in mine as I ride a 1997 Skidoo. Mine lasted 20 years from the skidoo factory.

 

That would be one massive peace of plastic, it would be also very expensive unless you could get it wholesale, you could use regular plywood, the original one did last several decades and as snow n go stated you could use T-bolts on the base, I used a steal plate with two nuts welded and ran the plate across the back between the foam and the plywood, but the T-bolts are less expensive and easier, I jut didn't have them on hand and wanted to complete my sled.

 

Or, another quick and relatively easy method can be used if your only issue is the mounting board and you do not want or need to replace the seat cover. You will need to purchase 1 or 2 T-nuts your choice. You will need to drill two holes in the wooden base one hole with approx. a 1 inch hole saw. and about an inch away from this hole drill a small diameter hole for the T-nut to drop into from just under the inside of the seat foam area. Maneuver the T-nut over the small diameter hole that you just drilled for the T-nut to sit in. You may have to press up on the seat foam to accomplish this. Best to drill the original mounting hole for the T-nut up from the bottom, this will make locating the 1 inch or so hole that you will need to drill much easier to locate. Press the T-nut down firmly into the board. Install the bolt for the T-nut up from the bottom of the tunnel into the T-nut this will draw the T-nut down firmly into place. I do not assume anyone's skill set, but I do say be careful around the heat exchangers if you have them.

 

Thanks for all the info guys. I'll just stick to replacing it with more plywood to make it easier and water seal the plywood. I'll have to buy some replacement hardware to remount it.