OK, I've just typed this out without reference to any books or info
sources
so, if I'm talking rubbish, I'll happily accept being shot down by others.
These are just my 'first-thought' opinions.

Basically I think it's for three reasons.
1. There is much less food available during the winter months so, to save
energy, point 3. happens.

Im not sure this is true. most aquatic insects spend the winter in the
lavae/pupa stages, ie caddise grubs, blood worm, damsel nymph ect.
they then hatch out into the winged adult in spring/ early summer. when
they lay there eggs.
As some of these insects spend 2 years in the lavae stage then winter
is the time of year when there is more natural food around.

2. A lot of the natural cover has died down leaving them feeling exposed
thus reducing their inclination to 'patrol'.
3. Their metabolism slows and they spend much time in a torpor (not quite
hibernation but getting on that way)
Re point 1. I believe that carp in heavily fished waters, with plenty of
groundbait etc being chucked in all the time, are tending to be more
active
during periods when you wouldn't expect them to be because of the
additional
food supply.

and Pike don't feed much in the Summer?
Or is it Myth?

I think this is 'probably' myth because ....
1. Most anglers don't bother with pike fishing until October or
thereabouts
so less catches are reported in the warm months.
2. The warm months are those when prey are most prolific, any sensible
pike
isn't going to go on a diet during that time. I recall plenty of
occasions
when bringing in a roach or other smallish fish (in summer) and a pike has
followed it to the net. Also, my keepnet has been attacked by pike on
quite
a few occasions, again in summer. They are there alright - and hungry.