Diesel engines in light aircraft are designed to run on Jet.
The reason for this (apart from availability at airfields) is the poor cold-temperature properties of diesel as opposed to Jet. Jet has a freeze point spec of -47 max. Diesel has a CFPP spec (not exactly freeze point but near enough) of -5C (Summer) & -15C (winter). That might sound enough, but diesel flow gets very sluggish within 5 deg of CFPP, and with a lapse rate of 3 deg/1000 feet (remember your met?) problems could easily be encountered while flying.
Contrary to popular belief, there isn't a huge difference in price either; the current price per ton for Jet is $236.75 and for Diesel is $224.63 (excluding road duty)
'Red' diesel appears to be cheap for 2 reasons - primarily as it does not incur road duty, and secondly, as Sensible noted earlier, it can have a higher sulphur specification, and is therefore slightly cheaper to produce. The current price per ton for red diesel is $217.13