NO. Mostly ...
The 5w winter rating means that the oil does not exceed a maximum viscosity in two very cold tests. A good synthetic 5w30 will often easily beat the 5w criteria, and almost meet the 0w criteria ( 5*C colder ) .
A conventional 5w30 will sometimes BARELY meet the 5w criteria, and not even come remotely close to meeting the the 0w criteria. Usually the cold temp cranking test is the harder criteria to meet.
Using Pennzoil as an example ... the 5w30 PUP is noticeably thinner ( less thick ... ) at extreme cold temps than is the PYB HM. Yet both meet the 5w winter rating criteria. Realistically, if the oil can pump, both will work about the same. But it will take more energy to crank the engine with the thicker oil. And if your battery is only gonna give you one shot at starting, the synthetic will pump easier.
The conventional Pennzoil HM yellow bottle 5w30 is as follows:
Pennzoil Platinum Ultra synthetic 5w30 is as shown :