Sometimes the difficult decision is not leaving until all efforts to improve the current relationship have been tried, but that does take two.
Your H obviously did snuggle when he was first with you, it's just that by now the lust biochemistry has drastically changed then what it was when you guys first got together & he's gone back into his comfort zone which doesn't work for you. He's gotten into the habit of disregarding your wants / needs in the affection / sex depts. Just talking to him isn't going to work unless he is willing to make the ncessary changes consistently so they become new habits.
He needs to realize that you are very serious about this & he can't just ignore your desires, he needs to be putting more into the relationship pot or he's going to be dating & flying solo again trying to find someone that is OK with his lack of involvement once the infatuation wears off.
There has to be a balance found between the two of you or the disconnect will keep growing. You say he thinks he tells you he loves you but isn't? Maybe he thinks you two are having a lot more sex than is actually happening too. It can be easy to lose track of time especially if there is a lot else going on in your lives or he does a demanding job.
It sounds like this may be a Love Languages problem, first of all. That would be a good book to read together to help get you past the impasse you have now. The 10 Second Kiss is a good one to use in combo with the Love Languages book.
Amazon.com: The Five Love Languages: How to Express Heartfelt Commitment to Your Mate: Gary Chapman: Books Amazon.com: The 10 Second Kiss: Ellen Kreidman: Books Is It Infatuation or Love?
.... When infatuated we experience a surge of dopamine that rushes through the brain causing us to feel good. Norepinephrine flows through the brain stimulating production of adrenaline (pounding heart). Phenylethalimine (found in chocolate) creates a feeling of bliss. Irrational romantic sentiments may be caused by oxytocin, a primary sexual arousal hormone that signals orgasm and feelings of emotional attachment. Together these chemicals sometimes override the brain activity that governs logic.
The body can build up tolerances to these chemicals so it takes more of the substance to get that special feeling of infatuation. ... When the chemical flood dries up, the relationship either moves into a loving romantic one or there is disillusionment, and the relationship ends.