The only constraint on running a saw in ambient cold temps is on the brittleness of your belts (probably not a problem, because your car has similar belts); on the thickness of the grease in the bearings (again if they turn they will warm up enough to keep themselves lubricated as they do in automobiles); the viscosity of the mineral oil if you are using a pump (if you are using a blade dipping into the oil, you should be fine as long as the mineral oil is a liquid (if you have a pump and its weak or uses narrow tubing, it may gag on thick mineral oil). One major disadvantage is that the mineral oil being thicker (at least until it warms up with friction) you will tend to carry a thicker film of oil out of the saw with the slabs (hence more cleanup, or just a longer wait in the cat litter before going to the soap bath). In my opinion cold mineral oil will cool and lubricate and bathe just as well as hotter mineral oil running at summer temperatures. My saw is in an unheated shop (at least until I fire up the wood stove) and the temp is usually around 40 when I get there in the morning, but the saw runs contentedly as the shop warms via wood stove and electrical space heater. One word of caution about cold weather and wood glues (wood glues don't hold as well unless they dry for 24 hrs at room temps. If exposed to freezing temps before they are dry they tend to release the stone. I've grown to try to keep my glue stubs from freezing (by taking them inside the warmer house). Obviously if you use wax to dop you will want to protect them from anything near cold until you are ready for them to release. My cab machine will run in winter months, but only because I use a gravity water system that I can feed from an electric tea kettle. Ah, warm water feels so good in that cold shop.
Horse laxatives are a lighter mineral oil than human stuff (at least the human version I buy at Walmart) and hence I prefer to use straight horse laxative mineral oil in winter but have no preference in the summer.
Given the need to do so, you could use a defrost heater from a refrigerator to heat your mineral oil above ambient but I doubt it would be necessary except for temps like Jake was discussing. Its not an accident that some folks live in New Mexico and not in the northern extremes.