It does not look cut from the one photo to me either.
Simple to check for a cut barrel though Spazz.
Measure it.
The barrel on my 1961 .38 Trooper comes in right at 4" from the cylinder face to the end of the square cut (no easily discernible crown) muzzle.
I also checked a 50s Model 357 and a mid 60s.357 Trooper. They both measure 3-15/16".
All three measure 1/8'' from the muzzle to the forward face of the sight ramp. There are some ballpark numbers to work with.
I sort of thought it had been re-blued from your previous post a while back.
Will make a fine shooter if it is locking six for six and if the mainspring has not had a pencil shoved in it.
I would personally re-polish the hammer sides bright following the advice on the Colt forum (leaving the sear notches and the firing pin alone). The pistol will look better for it.
The sideplate screw head under the grips at the rear of the frame will tell you what grips came on it originally. Rounded screw = service stocks - flat screw = target stocks.
Can't recommend spending the dollar amount for original stocks for this one though. Just an FYI if you run across a set cheap.
Pick up a copy of Kuhnhausen's manual on the Colt DA if you've never had one apart.
A proper fitting screwdriver, a wooden hammer handle, an old toothbrush plastic handle, and a very small screwdriver (for the bolt spring) are all I use to perform a complete frame strip.
Since it sounds like you bought it (rather than inherited it with the associated memories), just enjoy it after giving it a good once over with some 0000 and oil on the rough areas.
Set the re-finish money aside towards another Colt after learning what to look out for.
A few of us have been there at some point.
JT