"Prius batteries are guaranteed for 10 years and cost upwards of £3k "
MY 2002 Prius had an 8 year 100K mile on the battery pack and Toyota has consistently quoted me replacement prices of US $2400 to replace it (includes labor). This is from the dealership (price is 2x the cost of the part and labor is 4x sanity safe limits) who always rips you off.
"This morning it was around -3 Fahrenheit (so would be roughly -20 celcius). Haven't done any research on how the batteries take this kind of temperatures. Does anyone know?."
I have gone out into my driveway and my Prius tell me that it is -14 deg F and it has started fine. I didn't even see the turtle light that tells me it is running without electric assist (turtle is on until the system warm up enough). I think some guy in North Dakota blogged about seeing it on a morning where it was like -36 deg F or some such. In Ohio it does not get this cold and so far I have never seen the turtle.
As for your problems a couple states over. I know that a large vehicle is not required for life in america. I lived in the backwoods of West "By God" Virginia and took a Volkswagen pickup truck on some of the most muddy, rutted and impassable dirt roads that sometimes would swallow big 4x4 trucks. I never got stuck no matter how bad the roads were, because I knew how to drive in those conditions. A VW pickup has the same clearance (including the oil pan that sticks down below the frame) as a normal Rabbit (almost none).
I have had no problems on highways and side roads with the Prius even when our fine people didn't bother to clear roads and my entire journey to work (only a class 2 snow emergency) on the interstate involved clawing my way through 6 inches (or more in places) of piled snow while trying to keep track of what was road by the distance of signs and guardrails.