Most of the nuclear winter scenarios envisage all out use of the big old megaton bombs (which aid in stratospheric injection) all perfectly causing runaway burn off in built up urban areas - the reality is these days the use of more efficient kiloton warheads in ways which result in less potential for that level of burn off and while not completely relevant to nuclear winter reduced fallout and a significant number would be used against military targets in more remote areas rather than 100% usage against urban centres.
It would still be pretty grim and a lot of people wouldn't survive but not quite the extinction level event usually banded around - average global temperature drop would be more in the range of 3-10C.
EDIT: It is one of the reasons why there was a lot of shift towards more efficient kt warheads when as above with the big old bombs even a successful first strike against another superpower had a good chance of also ensuring your own demise.
And unlucky for Russia, global winds would blow most of the fallout their way