It is the old straight style. My Winchester book is just a little hand book that gives serial number/ manufacturer date ranges. I tried to get the forend off with no luck. I can't get it to slide forward enough to come out of the grooves from the receiver. It hits a piece of metal the forend band screws into. So I can't see the date of the barrel.
The entire magazine and forend has to come off.
Remove the magazine end cap (cross)screw. --> Be advised the cap is under spring pressure from the magazine spring, it has to be controlled as the cross screw is removed. Remove cap (it does not thread into the tube, despite having a screwdriver slot in its end. The purpose of the slot is either an intelligence test or is to tempt people to try to unscrew it and have to buy parts to replace the one they ruined. Truly, the caps/tubes werent threaded in since the 1870s.). Cap probably has small extension that engages a slot in the underside of the barrel, it needs to be turned enough to disengage the slot. Remove spring,
Remove forend cap screws (2), slide cap forward. Magazine ring, if it has a cross pin, needs to have the pin drifted out. If no pin, magazine tube should slide forward. It has to come completely out of the forend for the forend to be removed. If you twist it it may end up with zig-zag scratches on the tube. Oil it if needed to facilitate removal, they often are sticky or gummy or encrusted in place with old oil. If desired to remove the magazine ring for any reason, it rotates in its dovetail, it does NOT drift sideways like a sight. Many are ruined when some goob tries to drive them out sideways with a hammer and punch.
Once magazine tube is removed, the forend can tip downward at the front to clear the forend cap tennon then come out of its recess in the front of the receiver. Youll see that it cant come out without removing the magazine tube due to its being a machined snug fit around the tube. Once assembled though, they are pretty durable due to not being hollowed out.
Barrel date should be a 2 digit number stamped on the bottom of the barrel along with caliber and inspection marks.
So long as the tube isn't too crusty, they come apart fairly easily.