This could be a concern. Ducatis are often cold-blooded creatures.
a) How many miles (km) on the bike (and battery)? I find that 3 or 4 years is about as long as a battery lasts, but I do 12K+ miles (19K+ km) a year. Do you remove the battery for winter storage, or have it on a tender? A new battery might be something to consider soon.
b) How cold are you talking? Mine tended to be hard to start below 40°F (5°C) with the stock system. I upgraded the starting circuit with heavier leads, and added a dedicated ground. Those helped a lot. I also, during the cold season, keep it on the Battery Tender when it's parked at home, just to keep everything tip-top. At the ends of the season (April and Nov/Dec) it's often at or near 20°F (-7°C) in the morning, and that setup works just fine.
c) You're EFI, and IIRC you don't have a fast-idle lever or any such; you just have to depend on the computer to manage startup fueling and so on. That's probably to your advantage. Mine's an older carbureted model, so I have to give it a fair bit of choke in those colder ranges.
1993 Ducati M900 Monster "Patina" (259,000 miles, so far) -- 1995 Ducati M900 (wife's bike) -- 1979 Vespa P200 (daughter's scoot) -- 1964 Vespa GS160 (160cc 2-stroke) -- 1962 Maicoletta scooter (275cc 2-stroke) -- 1960 Heinkel Tourist 103A1 scooter "Elroy" (175cc 4-stroke)