What on earth are you doing "washing" a Ducati with water?
If its salty What on earth are you doing riding a ducati at this time of year?
They need caressing!
This is a bit like Weeksy's 748 wont start thread.
Ducatis do have pp3 size betteries. Any v twin is a lot of engine to turn over let alone when its this cold, both on the engine side and the effect of cold on the battery.
For the sake of the engine, bore washing with fuel, and also working with no load, its just not worth running a duke unless its going to get a good run out, this would also recharge the battery, as the amount of charging needed to replace the amount of power used to turn over is several miles worth.......