Mice probably are too short-lived, you want something larger (unless you are building a generation ship!)
Domestic mice have a lifespan of up to about 30 months. This is not very long for Mars missions that are normally well over a year at least. Additionally, I do not think that reliable gestation and parturition of mammals has been demonstrated in space.
Landing on Mars with an animal and bringing it back alive isn't necessarily much easier than with a human (and in some ways could be much harder)
At the very basic level of feasibility of orbital transfers, the situation is very similar to the sample return problem. Sample return from Mars still hasn't been done or truly committed to, even for sub-gram samples, because, while a rocket to launch from Mars and transfer to Earth doesn't require as much delta-V or as much acceleration as a rocket to launch from Earth and go to Mars (putting it in the readily possible category rather than being marginally possible with extremely flimsy multi-stage vehicles), it still takes a pretty substantial rocket to launch from the surface of Mars -- and that rocket (even if unfueled and using ISRU to procure propellant) must be landed softly on Mars. At small animal scale, it's likely that the various "minimum gauge" concerns of practical aerospace hardware might be the limiting factor on how small this mission can be, rather than the actual payload.
However, a small mammal, just like a human, needs to be fed (at least 70 kg/year for a small dog), to have its waste disposed of, to have oxygen supplied and CO2 removed, to be shielded against radiation, and probably to be supplied with space and stimulation so that isolation and crampedness does not lead to stress and cabin-fever that quite possibly causes death by malaise or self-destruction. This means mass.
For an animal, there are significant additional issues: A number of tasks, critically feeding and removal of waste, have to be automated, which means additional weight and moving parts and risk of unreliability, in contrast to astronauts who can do them manually or with simple tools that don't need 100% automatic, flawless operation.
There isn't much you can learn in orbit that you can't learn in LEO.
If your goal is to find out how long-term partial gravity affects animals (a critical thing which we do not, indeed, know, and which is hard to learn on Earth), it would probably make more sense to run an experiment in LEO with a space station centrifuge, tumbling-pigeon or tether-based satellite. You will still have many of the requirements, but you don't have to land and take off, and the delta-V requirements (and therefore how much payload you get for the rocket) are vastly improved. You may be able to have astronauts tend them, and the mission length can be adjustable rather than both fixed and very long. Radiation shielding (mass) is also not as much of a problem in LEO.
If your goal is to evaluate the various stresses involved in a Mars mission, the thing to do is probably to make a battery of experiments to analyze them individually on the ground or in LEO, combining with things that we know already, rather than actually doing the Mars mission.