Are the butterflies out and active at all times? Even cloudy days?

Yes

The butterflies are flying, resting, eating in a huge garden covered by some kind of plastic like a greenhouse so the outside weather wouldn't effect them (i think) because temperature at the inside is perfect for them

The butterflies are out and live in the garden area. Now whether they're active on cloudy days will depend on the butterflies. Its a beautiful place though and I highly suggest wearing bright colors. When we were there, butterflies landed on us, along with many other people.