In New England during the Winter, things slow down. Riding your 3 speed is slower. Not only is it harder to move because of having to be bundled up, but greases and oils thicken and can make it hard to simply roll your bike.
What was once a thin oil that would spill out of a bottle and work perfectly for a 3 speed hub, in the cold can stick things up. The change is drastic and enough to consider changing to a thinner oil if if you ride during the Winter months.
That being said, oil is oil and anything is better than nothing, but when it gets below 30 degrees, a thinner oil works better.
I run my Raleighs on oil. I use grease to assemble my bikes, but run 30 weight into the Bottom Bracket, hubs and chain. A good oiling before a ride can make all the difference in the world.
During the Winter months I use "Marvel Lubricating Oil" Different from the "Mystery Oil" that most mechanics are familiar with. The "Lubricating Oil" is for doing just that. Its thin enough to get into the hub and work. Its displaces water for less freeze up as well. The side of the can use to say "Good for,,,and Velocipedes" That was enough for me to give it a try. Actually it was the only oil in the house at the time.
Im sure that their are many oils on the market that will work as well. Checking the effect of the cold on your choice of oil can be done s easily leaving the bottle outdoors over night. Leaving the bike in a barn or a unheated garage has the same effect, it just cant be seen to be believed.
Choose a oil that is thin enough to do your job and don't forget to change back when the weather warms up again!