I was in that position last fall when waiting for the boat to go into the shop for engine work, I just wanted a month of protection and it wasn't real winter yet. I didn't want to transport and set up my full frame system which was at home, and tried to get by.
The trouble is the Morgans are pretty wide, the cockpit is too large to stretch a tarp over, plus there are all sorts of things sticking up, most notably the lifelines and stanchions around the perimeter. Without a frame to support it the tarp will end up being a 12 ft x 38 ft swimming pool liner filled with water (and then frozen ice where we live.) You need a frame to support the tarp above the lifelines and shed the water/snow or you are creating a swimming pool. I know in my case, just trying to do the minimum to get by a few weeks, just a couple of storms and the tarps I had tried to support with some lumber spanning the cockpit, it all collapsed and flooded, then froze. Not nice! I never did recover from it and the only way that it could be melted was to when they moved the boat inside in the heated shop.
Steve