I do Viscum album for many years now. Best time is March. The embryo is than at full ripening.
The main problem is that most of the green embryos die because they were kept in the dark for some time, or it was too early to put them on.
They need light the whole time while ripening and waiting for the birds.
More than one or two weeks in the dark can be fatal.
Then you need no shed or garage, they can stand some 20 minus easily. I had in most cases the first two leafs the second spring, though some waited two years or even more.
I think it depends on the climate and the tree they grow on. It takes here in 6b, seven to eight leaf sets until they flower. Each set is another year. With this plant you have just to count the sections, each is a year. Usually they divide at each section.
One time I wanted to be very clever not to rely on the sticky ooze of the berry and used some tape to hold them. Usually I loose a great part to rain and birds.
That year I lost all. They died because of lack of light. I used a non transparent tape in order not to overheat them.
Mistletoe starts best on very young bark. The reason why you see them on thick branches is the age.
I got most of the tricks from a botanist at a Botanical Garden here. He had more than hundred mistletoes on a very small apple outside. If you counted the seedlings, it could have been thousands.
No wonder this appletree was no more when I visited the garden ten years later.