I know this is an old post but I wanted to respond to it anyway because it always shows up when I search for tips about winter fly fishing in NH. I wanted to clear up confusion for others that this post might cause when researching winter fly fishing in NH. Below is a link to the the state of NH fish and games website that lists rivers in NH that are open for year round fishing. These can also be found in the NH fishing digest under the special rules section for rivers and streams.
https://wildlife.state.nh.us/fishing/trout-streams.html
On a more specific note, the river that the OP is talking about is stocked by the 3 rivers stocking association. They are very influential making it possible to fish the cocheco river, lamprey, and Exeter river year round. So if you find your self enjoying these rivers show them some love.