When I was there in 2008, everything seemed to be open on Saturday (I toured the Reichsburg and tasted wines at Rademacher winery that day). Be aware, if you are using public transportation to get to Hahn on Sunday, public buses run on a reduced schedule on Sundays. I found out the hard way; I was stranded for four hours in Beilstein waiting for the bus to come to take me back to Cochem (I saw everything of interest in Beilstein in about an hour). You can check the bus schedules on the Bahn website or on the website of the local transit authority, VRM.
There is a private bus line to Hahn, but it only goes from Cochem twice a day, at 2:55 AM and 4:55 AM. The rest of the time, you have to catch it at Bullay, ~10 min away, 3.65€.
BTW, it should be noted that, although referred to as a Burg (castle), the Reichsburg is not an authentic castle. A castle used to stand on that spot but it was destroyed by the French in the 17th century and the ruins were purchased 200 years by a Berlin businessman and rebuilt. What is there now is, as explained in the tour, "a chateau".