Boss Hog will be along shortly I'm sure, he knows the conversion like the back of his hand. There are also some good write ups with part numbers in the Cub- How To forum.
Fix your electrical system---make sure cables are in good shape, battery cables the right size, connections clean, bright, and tight, and I would bet money your starter needs servicing. Most of the time a 12 volt conversion just hides other electrical problems. If it is right it will start when it is cold.
12 volts does an amazingly good job of performing CPR on a dying starter.
Super A's theory is spot on. After spending a fair amount of coin on the 12 v conversion, down the road the starter will fail to behave even with 12 volts put to it.
You may be cash ahead just to drop the dough needed to have the starter rebuilt or replaced. Also as mentioned earlier. Make sure all your cable connections, both power and ground are serviced before condemning the starter.
Yup, as Al said, fix the electrical system. My Cubs are 6 volt and they start usually first spin even in the winter. Yeah, -30C can be a little tougher but it isn't any easier with 12v either. As Eugene said, get the battery tested and see if the battery will accept a charge. Also make sure that your generator is charging.
Start with all of your grounds, make sure that they are clean and bright metal. Check all the terminals for corrosion, cracks in the insulation, partial breaks etc.,. Once you find the fault, it will be readily apparent that a conversion is not required and it will probably save you a lot of money and frustration in the process. If you need to have the starter rebuilt I would recommend taking it to an old style repair shop or your local AC Delco Service Centre.
My hard start/slow cranking was because of completely worn out starter brushes. $10 or so and about 1/2 hour of time and it's better than any time in the 43 years we've had the tractor.
Don't do it!
Keep your tractor original.
Sounds like you have a bad cable or connection or maybe someone replaced along the way with undersize cable.
I have 3 Farmalls, all original 6 volt and they all start easily. When I have a problem, it's not because of the 6v system, it's the same problem you'll have with a 12v system, typically a discharged battery after sitting for too long.
Gerry