I think the first thing you should focus on is muzzle training. You can absolutely build up your dog's comfort with being examined, but firstly you should protect your dog and anyone handling him. I know the use of a muzzle can seem intimidating or like some kind of failure, but it really isn't. It's just responsible. Many dogs are muzzled at the vet, and every dog should be muzzle trained, whether they've nipped someone or not - just like crate training, you never know when it might be needed, and it's better to have a dog that's already used to the experience than expose them to it when they're already under enormous stress. Kikopup has a good video for getting started with muzzle training.
Secondly, I think you should reframe how you're looking at the snapping. Rather than thinking "my dog has a behaviour problem", try to understand what your dog is communicating. When dogs snap in the situations you're describing, they're very stressed and fearful. It's not as simple as not "liking" something. So, try to think about this as you working with your dog to lessen his fear. Of course he is loving and sweet when he's not afraid of being hurt.
Does your dog growl before a snap? Does he give any warning signs? It's common for owners to ignore body language that should tip them off their dog is about to snap - growling, a curled lip, lip licking, averted gaze. Some owners even punish these behaviours, which teaches their dog NOT to warn, and instead go straight to biting. This is not a smart move for an owner! You want to respect when your dog gives you warning signs. Never scold a growl. I would also do a bit of reading on dog body language in general - this book gives an awesome, brief overview of how dogs communicate friendliness, discomfort, etc. You mention that your dog "gives lots of kisses", which is typically more of an appeasement behaviour than a happy behaviour and makes me think he may be more nervous in general at the best of times.
> How do I get him not to snap when someone is taking a look at him?
Counter-conditioning and positive reinforcement. You aren't training your dog not to snap, you're helping reduce the fear that causes him to snap. To reduce fear, you need to build positive associations with the experiences that upset him, like someone handling his paws, bringing a nail clipper near him, examining his ear, or holding a dropper to his ear. I'm not going to lie - this is hard, slow work. My dog dealt with a series of very unpleasant ear infections and we went through this exact process. It takes weeks and months, depending on how regularly you work on it and how ingrained your dog's fear is.
This is a great video that shows the (accelerated) process of conditioning your dog to tolerate ear handling and medication. You can apply the same principles to nail clippers and paw handling.
This book really helped me.