I should say that there is not just one best time to cuddle, but there are several best times to cuddle. Felines you must keep this in mind. One of my favorite times to cuddle up with that human of mine is when she goes to bed. It is best when they go to bed that you go with them. Personally, I believe that the best method is to get on the pillow with my pet.
Now, my pet often doesn't like this, she will push me around and try to adjust my position to what she wants. I allow this at first, but I then move back the position I wanted originally. This may take a couple of tries, but eventually the human will give in. I am a feline therefore I must always get what I want.
Another great opportunity to cuddle is when your human is sitting on their thrown. You know that great porcelain thrown in each home. Your human may not like this so much. But there is little they can do while they are there. You can attempt to sit on their lap, they really don't appreciate this at this time. But oh fellow kittens we all know we must try anyway. Otherwise cuddle up against their feet. They may be much more affectionate with this approach.
I do believe that this feline has summed it all up with this picture. We all know that when our owners are wearing dark clothing that is truly the best time to cuddle with the human.
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