First of all, let's dispel a myth. Mars isn't really all that red and those parts that are red are due to oxides in the surface material; Mars is literally rusting.
This presents a problem because what that rust is actually doing is tying up all the oxygen in your atmosphere. Without plants to photosynthesise, or some other endothermic reaction, you can't release that oxygen back into your Martian atmosphere. So, you definitely need plants.
Trouble is, Mars gets about half the sunlight that the Earth does per square metre. That's not enough energy for most earth plants to grow, which does tend to describe what colour your Martian vegetation will be;
Black. Not just in the visible spectrum, but also probably in infrared, and definitely in the Ultraviolet bands. Why? Because earth plants are green because they're reflecting green wavelengths of light. Martian plants cannot afford the luxury of reflecting ANY light energy it gets; not if you also want an oxygenated atmosphere.
As has been noted, red plants may also work because the red energy is the lowest energy part of the spectrum (which is also why I put a probably against infra-red), but given the lack of sunlight there by comparison to Earth, I'd argue that black leaved plants are still going to out-compete the red ones, unless the colour has another benefic attached to it within the ecosphere.
This is assuming surface vegetation of course. In your question, you put forward the idea of underground water sources and vegetation; such 'vegetation' is likely to be fungal in nature, but that doesn't help you with an oxygenated atmosphere which is why I put this alternative.
The weather and volcanic activity of Mars isn't that likely to change all that much; a magnetic field implies that Mars may have a molten metal core, meaning that it's possible that the volcanoes could still be active but given their relative height and the layout of the planet, that's by no means certain.
Your atmosphere, if denser, will mean that the Martian dust storms could do a lot more damage than they presently can because although they look impressive on the surface of Mars, at less than 1% atmospheric density, they do very little harm. Of course, such a density isn't livable for complex life, especially humans, so your tradeoff in making the planet habitable is either much slower wind speeds, or more kinetic energy in them (and therefore more potential for damage).
As for the poles, just how 'frozen' they are would actually be dependent on what atmospheric density you apply. The denser the atmosphere, the lower the melting and boiling points of different materials are. The Martian poles are essentially coated in a form of dry ice, or solid CO2. You wouldn't have to make the atmospheric pressure too much denser to make it melt, or even boil back off to a gas. The water there is probably still going to be frozen, unless you're dealing with an ultra-dense atmosphere and you're not going to want to do that.
Would it still be cold? Most definitely, but then so is all of Mars. Again, to make it habitable, you now need to;
Increase the atmospheric pressure
Release a LOT of the oxides back into the air as O2
Have plant life continuing to do this via photosynthesis
Have water sources available - lots of them
Heat the ambient temperature to something more tolerable by humans
Once you've done all that, there's only one thing I can guarantee you; your planet won't resemble Mars much at all anymore.