Its good of you to ask as I expect a lot of folks will get the spring hiking fever this week. Hard to guess trail conditions this time of year. Its highly likely barring a sustained record stretch of hot weather between now and then that your intended hike is going to be a exercise in futility that will end short of the summit. Even if you do try it you potentially are going to make a mess of the trail and the hiking community will curse you and others hiking without snowshoes.
How do I make this prediction? There was fresh snow on the summits yesterday morning (5/1) with a deep snowpack in the woods around 4000 feet (48" at Gray Knob on Mt Adams on April 28th). Access to Gale river trail is via a seasonal Forest Service road that most likely will not be open yet as the frost is not out of the road. That means a couple of miles extra walk from RT 3. Gale River trail is on a north slope so the slopes are under trees and is not getting bright sun and therefore at some point the wet muddy trail is going to turn into wet sloppy snow turning into post holing. In order to burn this snow off, we would need unusually warm conditions and that frozen snow would need to turn into water which would cause near record flooding.
Do everyone a favor and consider some hikes farther south or some of the trails that have good southern exposure and open slopes so that have higher possibility of having melted out. Since I live up north I cant give you any southern NH summits off hand but expect others will. My go to early season hikes in the Whites are both in the Conway area South Moat and Kearsage North both tend to melt out early but also have stretches of potential icy stretches and the dreaded "monorail" (a large lump of wet ice in the center of the trail with deep snow to either side). Of the two, South Moat has a lower chance of monorail as the slopes are mostly open all the way to the summit. Keep an eye out for Welch Dickey reports. It is lower elevation and had good exposure. It also is incredibly popular and has been "hardened" somewhat from mud season by effectively paving it with rocks.
One other thing to consider is that if you are an early bird hiker, the snow pack may have solidified overnight meaning you will not posthole in the morning but as you are heading down that nice solid snow will get weak and then you will start postholing making your trip out a potential nightmare.
Keep an eye out on the various trail conditions sites, TrailsNH and New England Trail Conditions. Trails are melting out day by day so consider hiking on a Sunday so you can see reports from the day before. Just because there isn't a report on the particular mountain you want to hike consider other nearby peaks that have similar exposure. A good fill in for South Twin is Garfield.
