Is it possible hook up an aftermarket stereo in a 1992 Eddie Bauer Explorer if the wires to the radio have been cut?

the answer is YES, use a test light to find the + and - wires (should be one ground wire and two hot wires [one hot all the time for your clock & one hot only when the key is on]) in order to find which speaker is which, use a 1.5 volt battery to make a popping sound in the speaker (won't hurt the speaker) and then the solid color wire will be your positive & the wire with the stripe will be your speaker ground.