USA and Russia have around 1700 ICBMs each, most launching MIRV warheads in shotgun blast patterns, with each component consisting of a bomb of roughly 10 to 15 megatons.
We don't have hard data on the Russian arsenal, but there is a great deal of information on the US one. For the US, you're off by quite a lot.
Going by unclassified information:
The United States has 661 ballistic missiles. 431 of these are silo-based Minuteman III ICBMs, and the remaining 230 being submarine-launched Trident SLBMs. The Minutemen are armed with a single 300 kiloton W87 warhead.
This is a total of 129.3 megatons.
The Tridents are capable of carrying up to 12 warheads, but are treaty restricted to 8. There are two warhead options for the missile, the 100 kiloton W76, and the 400 kiloton W88. The majority are armed with the W76.
Depending on warhead mix, this totals 184 (all W76) to 874 megatons (all W88)
Thus, the US missile based force has a total yield of between 313 megatons and 976, probably on the lower end of that number.
By the figures you gave, the floor figure would be 17,000 megatons.
As for nuclear winter, most of the studies involving it require a "firestorm" effect in cities hit. Not only are most of the missiles on both sides probably aimed at the other side's missiles, airbases, and such (which won't create the firestorm needed for nuclear winter to occur), a 2010 Homeland Security study suggested that a modern city won't create a firestorm at all, even if hit with a large warhead.