It's not impossible (because that's a pretty high bar to clear) but I'd say it's very, very unlikely.
The reason is time. Multicellular life didn't become common on Earth until 500-600 million years ago (Life showed up on Earth very early. But it consisted of microorganisms). There are a very few possible older fossils of very simple (think algae sheets) forms of multicellular life. This is also past the point where oxygen was common in the atmosphere.
Mars never had that kind of time. When it dried out and froze, earth was still billions of years away from its first real multicellular life. For plants and animals to have shown up on Mars, they'd have had to appear much, much faster than they did on Earth.
Of course, stromatolites or other fossils resulting from single-celled organisms are more likely. I discussed the second part of the question, but fossils aren't limited to multicellular life.
Life seems to have showed up on Earth very quickly, but took a very long time for animals and plants to appear.
Look at the diagram on this pdf. The leftmost set of bars is Earthly geological eras, the one just to the right is Martian eras. Earth had a proper crust by the start of the Archaen, Mars by the start of the Noachian. That's a 300 million year difference or so. Contrast this with the three billion years or so where Earth contained only single-celled life.
Earlier cooling just doesn't provide very much time, comparatively.Source