Is a special version of oil required for winter maintenance?
It's obvious you're a newbie to this, so don't take this as a negative.
The first thing to take into account is whether you intend to hunt in cold conditions.
Depending on where you live, that's a very valid question, because some Provinces/Territories open their seasons in mid August, in some regions.
Other Provinces don't open their hunting seasons until November.
Every answer you get here, other than a few, will be different and valid for that person's needs.
Those needs may not mirror your own.
The biggest issue you can get with winter lubricants and firearms is USING TOO MUCH LUBE, in the wrong places.
Many folks hunt without any lube at all on the working parts of their rifles. They've learned, either from hard experience or from a good mentor no lube for a few shots will not cause damage to the inner mating surfaces, and will not attract detritus or parts to malfunction because tacky or frozen lube has gummed up proper operation.
Graphite is OK, especially for semi auto firearms, or the full auto firearms used by the military. It works, but it's messy.
The next thing is, why do you want to lubricate the firearm? Are you trying to prevent rust or make sure everything functions smoothly?
How much lube do you require? By that I mean quantity on hand.
Most lubes sold as firearms lubes are just off the shelf products, packaged in smaller containers at horrendous prices. This isn't always a bad thing, because people with only one or a few firearms don't need much, and if storage is an issue, the smaller container may be worthwhile.
Some folks know a lot about lubricants, because of work related requirements, most just listen to the "counter jockey" at their LGS or Big Box store, who doesn't know any more than you do.
I've been at this for 60+ years, used most operating types of firearms under all sorts of environmental conditions, and one of the first things I've learned the hard way is that lubricants create more issues than they fix in most cases.
There are some very light, silicone based spray lubes available off the shelf at most Big Box stores. They cost about a quarter as much as a similar or even identical product that comes in a firearms labeled container.
A quick spray on the back of the locking lugs is all you need for the working components.
Trigger assemblies should be dry.
Bores should be dry.
The rest of the rifle should be dry.
You don't want lube in the bedding of your rifle it will cause accuracy issues.
Keep your rifle clean, and minimally lubed during hunting seasons, hot, cold, dry, or wet.