"Over the Enterprise-Lewiston Highway from the Washington State Line, southerly to its junction with the Wallowa Lake Highway, OR82, in Enterprise."
~ ODOT, Descriptions of US and Oregon Routes, March 2007
OR-3 was designated in 1932 when Oregon's route numbering system was established, routing the highway over what was then known as the Enterprise-Flora Highway #11. This highway currently connects to WA-129, but at first the highway was only designated to Flora, curving to the left of current OR-3 into the small border town. However, by 1941, work was being done to open up a highway to connect OR-3 to Washington (their part was called the Dodge-Clarkston branch of PSH 3), and the highway was routed (perhaps only temporarily) through the city of Paradise over poorly-maintainted mountain roads, and rejoining today's WA-129 south of Anatone. Finally, when both states' portions of the highway were completed, Oregon's part of the highway was redesignated the Enterprise-Lewiston Highway #11, retaining the OR-3 designation.
The Oregon portion of what I believe to be old OR-3 through Paradise is still intact, remaining as Paradise Rd. and extending through Paradise from Jct. OR-3 near Appleton to the Oregon-Washington border near the Kuhn Emergency Landing Strip; another possibility is Rye Ridge Rd., which you can see is the southernmost road that branches off of Paradise Rd. on my map. However, Washington's alignment of PSH 3 DC appears to be no longer intact on a multitude of maps I've studied; apparently it was some sort of unimproved forest road, which doesn't leave much information as to the actual routing.
The first possibility is called Park Rd. (designated in red), which currently leaves WA-129 and only serves Fields Spring State Park. The second is a combination of Fountain Rd., Smyth Rd., and Monterey Ridge Rd. (Asotin County Route 206) (shown in green), which peters out in the mountains. The third routing is all of Shumaker Rd. (Asotin County Route 276) and Montgomery Ridge Rd. (designated in blue), which is the longest route and partially parallels the Grande Ronde River; this route would be more conducive to the connection to Oregon's Rye Ridge Rd. I have absolutely no clue as of this point, but I will look into it and also put up a map scan in the future.