The worst weather of the year is often in February, and there is often plenty left in March. Your experience may vary of course.
The Cotswolds is an outdoor area to visit. If you want to be inside pubs they are everywhere in the rest of the country and you can be somewhere with museums and other indoor activities. There aren't a lot of indoor activities in the Cotswold area, especially when you are in the real Cotswolds, not the periphery. People go to the Cotswolds, an official Area of Outstanding Natural Beauty, to see the scenery and architecture. That's less fun on a cold, windy, wet, muddy day. The days are still relatively short. Gardens are closed as well as having nothing to show, the trees are still all barren, the golden Cotswold stone buildings look much better in sunshine or at least dry. The walking paths which show off the beauty will be muddy and possibly slippery.
Now that's all based on my experiences living there. I know you asked Jennifer and I expect she'll chip in from her experiences visiting there.
Go there if you want - I'm sure the pubs will be glad of your trade - just she and I want you to understand what it is very likely to be like - forewarned is forearmed.
I did ask a number of questions up in my first response to your Cotswold thread, asking you what you hoped to find there. I'm sorry you didn't reply because they were to help focus on where to suggest to you and what to do. I've had to just paint the negatives of March - I'd like to tell you the positives of what you are after but I don't know.