Hang in there! You are just starting, you'll be amazed at how much better you are doing at the 6, 12, and 24 month points. Dancing cheek-to-cheek is out of the question with my dear wife (DW), though sometimes I'll dance with my chin on the top of her head. Sometimes my DW wears very tall heels, and sometimes flats, the variety is fun. We finally had a very tall lady in our area. With heels she was within 2" of my height. My wife, all happy for me, said "Look, you finally get to dance cheek-to-cheek!" Now that I'm more experienced (3 years and hundreds of hours of experience) I do find one advantage to taller ladies: It is easier to see if they are smiling. Other than that I don't find the fun correlates to height. There are some steps that are easier with taller ladies, and some with shorter ladies, but it is a small number of steps that both can't do, and those tend to be show Tango steps.
Just to check, I assume you are doing close embrace? This would likely not be a problem in open embrace.
I'm not an instructor or an expert. My guess is it is less an issue of height and more of learning the finer points of leading. Here are some things that helped me:
Stand with your chest touching the edge of a door and keep your body straight. With your weight on your heels, your toes will actually go past the edge of the door. As you put more and more weight on the balls of your feet, you can get your feet almost a foot away from the door edge, and still pull your chest off the door (without hands). My instructors have said you want about 3/4 of your weight on the balls of your feet -- that gives your feet some space from the lady's feet, even if she is not doing the same.
This seems to be hard for the taller guys. Don't bend over your partner! You want a straight body for every height of lady. If you bend over, she is going to have to bend back a bit to conform to you for close embrace -- which means she'll put her feet closer to yours. Once I quit bending over the short ladies (didn't "need" to bend as much for taller ladies), I found it as easy to dance with short ladies as tall ladies.
Before you start: Switch weight between feet until you are sure you know which foot the lady is on. Then you'll know which of her feet are free to step with. If you just step, many ladies can sense that and quickly adjust, but they'll be a little behind then. Something I didn't learn for a couple of years: I was changing weight so smoothly that the ladies were having trouble detecting it. My close embrace was not going well. The instructor taught me to make a faster, more definite change of weight. That sends a clearer signal to the lady and my close embrace has gone much better.
Be sure to lead with your body, not your feet. To step, your body starts going forward. For shorter ladies I was tending to lead a step by bending over them. A couple of tips that helped me: "Move your heart towards her" and "Wait, wait, wait to step."
This has taken me quite a while to develop and I'm still working on it. As a beginner, I would lead a step, and then it was "Look out here I come!" It usually worked because usually the ladies were reading me well enough to get out of the way, but there were definitely some accidents, too. Ideally you start to lead something, sense if the lady's leg and foot are where you want them to be, and then move yourself accordingly. A great moment for me was the first time I could tell my wife's leg was stiff and not loose for a leg wrap well before the leg wrap. It's also great when I can sense the lady didn't step as I expected, and suddenly I need to go to plan B (it's perfect when she has no clue a "mistake" was made!).
With someone I don't know I start with weight shifts, and then start with a back step or side step to be sure we are in sync.
My first year instructor told me many times to take smaller steps! Something that might not be intuitive, take smaller steps to dance faster. BTW, ladies tend to be more flexible than we gentlemen. Some ladies have challenged me to a step size contest, and I have been amazed how big a short lady's steps can be!
Often short ladies say they wish they were taller to me. I always tell them they are a great height. Beauty and dance skill exists in a wide range of heights.
It would be great to hear insights you gain in the future.
I'm 6'5" (195cm) I've just started dancing (like, literally 4-5 lessons so far) and I've found that it's a *lot* easier, a lot less awkward, much more enjoyable, and I tread on less toes (due to different stride length, I think?) with taller partners. Unfortunately, the majority of learner followers I've met in London are significantly (more than a foot) shorter than me so far. It's dissuading me from continuing lessons a bit, to be honest.