I think it is OK to keep a secret, if you want, from your SO, as long as the keeping of that secret does not harm him or her. Everyone should have the right to privacy. If partners have separate mobile phones I do not think either has the right to pry. What I do not think is OK is lying. I do not tell my SO every sexual fantasy I have. She would find that boring and really TMI. But I do make it a policy that if she asks me a question I answer it truthfully. She is completely aware that I am transgender and highly supportive so it isn't the OP's situation. I would suggest to the OP that if the SO asks, tell the truth! Marriages can survive and even thrive one partner being transgender. Very few marriages survive lies. Also, bear in mind that if cross dressing is a large part of your life, if you have a combined income and are spending surreptitiously on women's clothes, if you are telling your SO you're just stepping out for a movie and instead step out en femme, you are establishing a pattern of lying that will disrupt your marriage sooner or later. Be careful. If you start lying it becomes easier and easier and, eventually, more and more catastrophic when your SO finds out. Bear in mind she's probably going to find out, sooner or later.

If you think your SO will dislike your cross dressing maybe you can arrange the type of understanding that Dan Savage suggests to wives who don't like their husbands viewing pornography. You pretend you don't do it and when she runs across evidence that you do she pretends she hasn't seen it. You are careful that she doesn't find evidence of it but you and she understand that everyone makes mistakes. This is the polite way than many couples negotiate behavior that they do not like in their partners, from watching pornography to having lovers. It does require maturity and self-control from both partners but it is a quite common way of dealing with problem areas in a relationship.

I don't think any of this is easy but the destruction of trust in a relationship is very often a relationship extinction event so trust needs to be treasured.