Yes! Opossums like me do dream as do many animals. We exhibit REM (rapid eye movement) during sleep which is associated with a dream state. However my dream state is probably very different than yours. Humans dream in visuals sometimes with sound. 

Sight and sound are among a human's most important senses - it is natural for your dreams to mirror life as you perceive it through your senses. But for me, sight and hearing are not my most important senses; they may not play any role at all in my dreams.

Smell is the sense I rely on most heavily - my sense of smell is among the best of any animal on earth. It is therefore likely my opossum dreams are smells only, no visuals no sound.  

Imagine you are sitting in a chair blindfolded wearing ear plugs and someone waves a freshly sliced apple under your nose. That fragrance might give you a pleasant feeling.  My opossum dreams may be similar. 

Because my sense of smell is so extraordinary dreaming of that smell would likely illicit a sense of contentment or pleasure you can’t begin to imagine.  A good dream for me might consist of a variety of smells like a pear, grapes, or blueberries, while an unpleasant dream might consist of the smell of a fox or coyote. 

So, yes opossums like me do dream. Much like humans our dreams are shaped based on our experiences - the good & the bad - in the awakened world as we perceive them. 

Works consulted:

Sleep in the opossum Didelphis marsupialis; Henry Van Twyyer and Truett Allison Electroencephalography and Clinical Neurophy: Volume 29, Issue 2, August 1970, Pages 181-189.

Monotremes and the evolution of rapid eye movement sleep; J. M. Siegel, P. R. Manger, R. Nienhuis, H. M. Fahringer and J. D. Pettigrew Neurobiology Research, North Hills, CA, University of Queensland, Brisbane, Queensland, Australia 1998.

The animals that could be dreaming  3 September 2023 Carolyn Wilke  BBC from KnowableMagazine.

And of course my own observations and all of the opossums I have been privileged to know over the years.