I'm no expert on drawing reptiles, but I looked up a bunch of references to make this! Which is, by the way, my #1 tip for drawing animals you're unfamiliar with. It gets you much better results than trying to draw from memory. :)
I went for a (simplified & stylized) boa constrictor look for this. Of course, different species would look very different! Overall, I'd say you need to lengthen the body (don't be afraid to curl around! It doesn't need to be straight across the page) and define the head better. I tried to include a step-by-step guide for that; hopefully it makes sense!
For non-snake specific tips, maybe try using thinner lines so you can include finer details? If you like the look of thick lines, you can always have those for the overall outline of the snake, while using a thinner brush for inner details (like the eye or scales). If you're having trouble keeping the lines smooth, increase the 'smoothing' in the brush options! It's a lifesaver, and I imagine it would be especially helpful when it comes to the smooth curved lines you'd need for a snake.
Let me know if you have any questions or if you have trouble reading by handwriting. :) I hope this helps!