The ideal way, from the plant's perspective, to overwinter these if to have them in a tropical house with all the time summer. Most of us do it with far less than ideal conditions, but a testament to this vine's will to live is that they come through anyways.

Whatever you do, prepare for a naked plant with dead vines, esp. after a frost. These are true tropicals, meaning they don't much care for anything under 60°F and dry air. This means that the leaves will fall. All of them by springtime. You will be tending a pot of mangey looking life until March. But, if you were to look underground at the roots, you would see large storage organs that will wait for the next warm, moist time to regrow. So don't let it get bone dry, because the roots are still alive. If you keep it cool, don't let it freeze (again in this case). If your garage gets close to freezing, it might be better to stick them in the house. Depending on how much foliage is left on top, you can either keep them near a window (if the plant has say, 25% or more of its leaves) and watch them fall off. This means that you will keep the soil somewhat moist until they are all down, then only water to prevent the soil from drying out fully. This scenario makes sure that the plant is not forgotten to dry out completely in a cold dark garage.

If the vine looks dead, with just about every leaf down, then it can be put in a cool dark place to lick its wounds until late Feb. Make sure the soil is sort of dry (but not bone dry), and try to keep ventilation on it so that fungi don't take up residence in the roots. Just good air circulation is fine, no need to run a fan on it. Keep an eye on the bottom where the frost is less likely to have killed everything, and when you see green pointy things in late Feb, place the plant in the strongest light you have. (Don't take the plant out of a cellar with 1/2inch growth and put it in full sun, this fries the new growth.) Get it used to strong sun.

In any case, I would wait until you see what you have left before pruning. These bleed a white sap that provokes a reaction in some people, and you may want to keep some of the vines for scaffolding for next year's plant. Throughout the winter you will notice some parts that wither and shrink and become brittle. This is dead and can be removed as you see fit to do it. Good luck. If you want to try some from seed, send an e-mail. I'll have ripe seed after the new year. The colors are varied though, so if you have your heart set on pink, do not grow it from seed. The pretty pink ones are hybrids and the resulting plants have flowers from almost pure white to dark pink, with a few that have pink/white blossoms.

I overwintered my Mandevilla and it did fine in the downstairs garage(we put light on our plants w. a timer that we overwinter). When the M. was brought out for the summer, we had a bad hail storm (first one I have seen in this area). The M leaves were terribly bruised and all were eventually replaced w. new leaves. However, my M only put out leaves and blooms at the top of the plant i.g. at new growth. I asked my local gardening store if I sh. cut it back. Yes was the reply.
Was this the right thing to do? e.g. Do mandevillas bloom on only new growth. I had many flowers all on top of the plant and onto my roof!