I love snuggly cats too.
Our Burmese who is 15 this year has never liked to be picked up or cuddled. From the first day we brought him home he hated it.
He is though extremely affectionate and loves to sit on you and be stroked. Every morning he will make a complete fuss of us, head bumping away, following us constantly around meowing for attention and sits with me all the time.
Because he is so affectionate I often 'forget' or can't stop myself from picking him up for a cuddle but he immediately stiffens and the claws come out.
I often wonder why he is like this. I remember when we got him from the breeder her house was immaculate and she brought him in from outside so he was obviously kept in a pen. Maybe this lack of socialisation is the reason why.
Our older Burmese who has passed away was the complete opposite. He would cry to be picked up, would fling himself at you if you didn't and loved to be carried around like a baby.
When we got him from the breeder all the kittens were running around and getting up to all kinds of mischief. They were so cute! The breeder's husband used to take it in turns with the kitten to carry them around in his cardigan pocket
I'm pretty sure socialisation plays a big part.