I think it's the other way around. Winter weight is the base stock and the additives keep it from thinning out as quickly.
Ie, 5w-20 and 5w-30 would have the same base.
With mineral oils that is often the case. Mineral oils naturally get more viscous faster as they cool compared to modern synthetic oils. So in order to get tighter viscosity ranges, additives are used to either thicken thinner oil at high temperatures or thin oil at lower temperatures.
Modern synthetic oils tend to hold a somewhat tighter range of viscosities at various temperature ranges than mineral oils by default, hence why 5W-30 synthetic oil is so common, but 5W-30 mineral oil is not. To make a 5W-30 mineral engine oil, you can either nerf a 5W-20 at higher temperatures, or try to thin out a 10W-30 at lower temperatures. However, a synthetic oil can easily be made to meet a 5W-30 specification without the use of a large number of additives. If you want to take that and make a 0W-30, sure you'll need a number of additives.
But if you want to make a synthetic into a 10W-30, you need to find a way to nerf it at low temperatures. The reality is there simply isn't any point. The whole advantage of 10W-30 mineral over 5W-30 mineral historically was that 10W-30 was cheaper and contained fewer additives, and thus lasted a bit longer. But with synthetic, it is literally more expensive to make a 10W-30 than a 5W-30, and given the higher additives required to make it into a 10W-30, there simply is no technical advantage except in perhaps some very rare and unusual scenarios.
The whole [X]W-[Y] naming convention for oils is outdated in my opinion and really should be updated. All oils get thicker as they get colder, but some oils do it to a a lesser degree than others. Really the proper way to identity an oil's viscosity is using the units of centistokes and centipoise.
In order for an oil to be considered a SAE viscosity grade 30, it has to have a viscosity at 100°C between 5.6 and 9.3 cSt (note this is a simplification). In order for that Grade 30 to also be assigned a W viscosity grade, it is then also tested at various temperatures to chart viscosity, and then is compared to a table (per SAE J300) to determine what category it should be placed in. For example, if our grade 30 oil has 6200 cP or less at -35C, it is labeled a 0W. If it exceeds 6200 cP at -35°C, it is then tested at -30°C. If at -30°C it is 6,600 cP or less, it is labeled a 5W. If not, it is tested at -25, and if it is 7,000 cP or less, it is labeled a 10W (and so on). Note this is a simplification, and I'm leaving a lot out.
By definition a 5W-30 oil meets all of the specifications of a 10W-30 oil. However, per SAE J300, if an oil passes as a 5W-30, it must be labeled as a 5W-30 and cannot be labeled as a 10W-30, even though it passes every other criteria to be considered a 10W-30. A 5W-30 will perform as well as a 10W-30 in most cases except that it also performs better at lower temperatures.
For more detail, I highly recommend reading through the J300 specification. Technically it is copyrighted, so I won't post it here. That said you can find it online pretty easily. Wikipedia also has a pretty good summary of SAE J300:
https://en.m.wikipedia.org/wiki/SAE_J300
