Winchester Nickel Steel was introduced for the Model 1894 rifle about 1896; with a reported ultimate tensile strength of 100,000 - 108,000 psi with an elastic limit of 81,000 psi.

Winchester Gun Barrel Nickel Steel for rifles was surely different that the nickel steel used in shotgun barrels
Report of Heat Treatment of Barrel Steel Rolling, 1902
http://books.google.com/books?id=YzhUAAAAIAAJ&pg=PA181&lpg
From Bethlehem Steel Co.
Carbon - .50%
Manganese - .77%
Phosphorus - .026%
Sulphur - .037%
Nickel - 4.0%
Chromium <.01%
Molybdenum <.01%
Tensile Strength - 107,000 psi

Midvale Steel Company c.1900 Nickel Steel
Carbon - .59%
Manganese - .765%
Phosphorus - .027%
Sulphur - .03%
Nickel - 1.57%
Chromium - .065%

The analysis would confirm Mike Hunter's statement
https://winchestercollector.org/forum/general-discussions-questions/receiver-steel/
Winchesters Nickle Steel had 3 1/2 % nickel and .30%-.40% carbon. I know that Winchester sourced this steel from the Midvale and Crucible Steel Companies.