The early Explorers had a couple of trans coolers so just the fact that you have a cooler dosent mean you have the tow package- 3.73 with the L/S was part of the package if I remember correctly.
Two coolers avail for the trans: first is a smaller cooler in front of the radiator on the passengers side, Super cooling has a larger square cooler on the drivers side, and a full shroud- that is the super cooling package and I think was included in the towing package but not sure.
From my navajo sales brochure: Towing package: upgraded engine cooling,limited slip differential with performance ratio(3.73), trailer wiring harness, heavy duty flashers(requires automatic transmisson)
This is all from the 91 Navajo sales brochure but should be the same for the explorer.