In my game players are able to push objects. I was looking for an easy way to make it such that if an object has wheels it is easier to push...

When a player runs into an object they generate an amount of force equal to their strength time 10. So, with 10 str. they can push 100lbs. Would it be as easy as just calculating the mass of the pushed object as Mass*wheelCoefficent if that object has wheels? Is 0.25 a reasonable coefficient for this? Would differences in wheels make a significant enough difference to make the coefficent specific to a type of wheel or would this just be unnecessary data clutter?

Since you posted this in Game Design, approach this the way a game designer would. How long do you want the
wheeled player to take to push the wheeled object up a ramp of known length, versus how long it takes to
push the unwheeled object up the same ramp? Just make the ramp, and push the object, and time the speed
based on your game design objective.

Would it be as easy as just calculating the mass of the pushed object as Mass*wheelCoefficent if that object has wheels?

Pretty much yes.

A more physically accurate version of that equation would be: Weight * FrictionCoefficient.

And from this we can see that you are basically trying to say that having wheels means a reduction in the amount of kinetic friction and therefore makes it easier to push.

Would differences in wheels make a significant enough difference to make the coefficent specific to a type of wheel or would this just be unnecessary data clutter?

That's up to you really. It depends how complete and accurate a model you are building. Potentially there's a lot more to modelling wheels to take into account (diameter, material, tread, axle friction, temperature, tyre pressure - to name a few).