Easter is a variable feast (excuse the pun) in 2 ways.
It can fall in late March right through to late April. The date doesn't necessarily effect the weather. But will bring more or less daylight.
Secondly is the weather. I have done something outdoors on Easter Monday for the last 40 years (not cycling related) and am very aware of how different the weather can be. I live not far from the NLs in Essex and have known snow, but that is rare. Last year it was stonking hot, with sunburn all round. The year before it was wet, windy and cold. So no advice from me about the likely weather, although chilly Easterly winds do seem to be a fairly regular feature.
One problem you may have is if travelling light is carrying your gear if the weather suddenly turns warm. You need to find space for leggings, vests, jackets, overtrousers, etc. Sounds obvious, but setting out fully clothed with bags full could bring a problem in the unlikely event that the sun shines.
Edit: By the way, my vote goes for doing it.
Cycle-touring, Expeditions, Adventures, Major cycle routes NOT LeJoG (see other special board)
Loving it, there’s something deeply satisfying in taking on the weather and beating it. With the right kit, a bit of thinking and planning the worlds your oyster, and in my opinion some of the best experiences come from the worst conditions.
I think everyone else has pretty much summed up the same sentiments in saying go for it, don’t be too ambitious, have a back up plan and make sure you’ve got the right kit for the predicted weather. Personally I’d rather be shedding layers than be cold and rather be carrying kit and not using it than wishing I had something I later needed, but most importantly, take the time to enjoy the experience.
Oh, and don’t tell the normal people that you went camping in the snow at the weekend or you may well get some funny looks!