As others have mentioned, check for bad ground. That could be the reason it wont start. However, that's probably not the reason it died. The oil does concern me, check the level of both engine oil and hydraulic. If the oil pressure dropped, because of a leak, then the engine will save itself by shutting down. If you think its hydraulic oil, that shouldnt shut down the tractor, but is cause for concern since you need to find the leak anyway.
Since its cold, could be a dead battery. Jump it with a strong battery, like from a pickup. If it starts, then its probably the battery. I just had to do this about a month or so ago.
When it shut down, did it do anything like idle down, loop (rev up and down), anything weird like that? Or was is idling and suddenly stopped?
The smoke at startup is normal, unless it's excessive.