At 3 months old he/she is probably just feeling comfortable in his new home & starting to open up a little.
My puppy Vash is 4 months, he only snuggles when he's too tired to try to escape, or when I've climbed into his ex-pen with him. The rest of the time he's too busy sniffing around looking for treats or wanting me to play with him to snuggle.
When I brought Vash home from the breeder he stuck by my side constantly, I couldn't move an inch without him following me, It made getting him accustomed to touching simple because he'd just lay in my lap and wouldn't move out of it or explore, he wouldn't eat much (certianly nothing besides treats), 2 months later he's hoping up in my lap, going off into places when i'm not looking, barking at his friends (dogs) when we go on walks, gobbling down any scrap of food that happens to touch the floor, ect.
He's still pretty much a "saint" as puppies are concerned, his teething hasn't resulted in any damaged furniture, he doesn't bark a whole lot (for a sheltie), he doesn't really pull much on the leash, and he plays fetch without any training.
That said, he has gone through a number of personality changes over these past few months. He's become more confident in himself and in me, and as that's happened he's developed new personality traits and behaviors (some good/some bad).
The worst change honestly was when he stopped whimpering when he had to potty and started barking. I was a little slow in catching on and that resulted in about 7 accidents in the house that day.