The high summits of Vermont (all trails above 3000') are closed by the Green Mountain Club due to trail erosion concerns due to ground thawing round plus water run off due to melting snow and rain. This is mid April (tax day) to memorial day. I would guess Katahdin is closed for the same reason. In the Adirondacks, the trails are not closed, but they (the hiking clubs) do discourage mud season hiking in the high peaks, especially the most heavily trammelled ones like Algonquin. It is worded voluntary restraint from hiking. In the live free or die state, I am not aware of any such restrictions. But be aware of trail erosion concerns and be prepared for full on winter conditions in late April, especially above tree line. That time of year can be especially deceiving as you can get 70 degree afternoons and a blizzard the next day. Trails can be especially icy and messy (old stale snow and mud). Bring traction devices, gaitors. In general, seek out ridge trails rather then ravines since they drain better, try to stay on the rocks, don't go around muddy areas creating side trails, etc... . I like to go to the northern presi's that time of year out of Appalachia if I am hiking. The airline trail is generally pretty well drained. I don't recall Lowe's path being all that muddy either. One of the best days in the mountains ever for me was climbing Madison & Adams in late April after 3 feet of snow fell in the mountains mid week, then by the weekend valley temps were in the 70's. It was tough going with snowshoes but absolutely beautiful.
edited to add: above all, stay alert and don't get lost. There are allot of SAR stories that time of year.