Hope this isn't off-topic; seems to me that it relates to a lot of what's here. I saw a profile on OKCupid, a woman who described herself as " in a domestic, asexual, platonic polyamorous relationship", and named the guy she's living with but didn't say if she's married. I guess polyamorous would preclude marriage. I was intrigued by the "asexual, platonic" part, but doesn't "polyamorous" kind of clash with those?
@johnm29: Not at all! Polyamory doesn't mean the same thing to everyone. At its most basic, it just means that you have the ability or inclination to ethically participate in more than one relationship, and the definition of relationship is very broad. Think of what monogamous relationships are like. Some couples have sex, some don't. Some do everything together, some live mostly separate lives. Some are okay with their partners cuddling others, some are not. Every relationship is different according to the people in it, and it's the same with poly.
It sounds like this woman is in a committed relationship with someone she feels connected to on a practical level, but not romantically or sexually, so she is looking for other partners to fill those roles for her. It doesn't really matter if that means marriage or not. To find out more, you're just going to have to use those communication skills. This is not directed toward you in particular, but I personally can't stand it when someone makes assumptions about me based on my relationship status. Assumptions are the enemy of communication.
@johnm29, Oh man, no. You can be poly and married, poly and asexual, poly and highly sexual but have a "platonic marriage" (i.e. have a life partner you don't have sex with, and other partners you do have sex with). At the risk of oversimplification, the only things that are truly "unpolyamorous" are committing to love only one person, and (by culture) not being ethical, transparent, and compassionate with your partners (e.g. not telling them about each other).
@Bruced I appreciate your approach of making sure any cuddling you do is in support of your marriage, meaning your wife's feelings about it are of the utmost importance. I caution you to not go overboard justifying your wife's feelings of fear, insecurity, and jealousy. In my experience, if she is coming from this place, she will say things like, "Anyone would be tempted! Being intimate with another woman is a slippery slope, right? I'm not crazy for thinking that, right?" And then the focus becomes on reassuring her that her position is reasonable. "Yes, anyone would be tempted. No, that makes sense." In reality, I'm sure you are 100% capable of going into a room, cuddling with another woman, and behaving yourself. Saying anything that undermines this truth is not in service of your marriage, I don't believe. Her meeting your cuddler is great; more information reduces jealousy. If she's in the room, you need to be able to relax; it has to be because she's more comfortable being in the room than not in the room, full stop. Someone women would be more comfortable (less jealous) being outside the room. It's just an accommodation for her comfort, nothing else, not "keeping you honest" or whatever. Also, you getting your needs met is primarily about you, not the both of you, and her role should be primarily to support you, and secondarily to overcome her own anxieties as necessary for that.
I joined this site while monogamously married and in a similar situation; my marriage ended, and I now identify as poly. So I may be biased, but I did my best to write that paragraph without a poly bias or a "bad marriage" bias. Some things are universal. Insecurity that isn't owned as a partner's own insecurity (to be compassionate towards, of course) but is projected outwards onto the situation or the other partner is toxic, and I'm not saying that's what's happening, but it's something to look out for. If I were writing from a personal, poly perspective, I would say this level of concern about cuddling is extreme — though common and reinforced by our culture — and it's probably more than I would be able to handle, even if I were to be in a sexually and romantically exclusive relationship again. Think about how crazy it is to be scared to talk to your life partner about your physical touch or affection needs (as I was), or even admit them to yourself, potentially for the rest of your life, because your partner is supposed to meet all of them, and they can't (or just don't want to!), and how much would it hurt them (and you) to be fully aware of that, etc. etc.! If I were to draw more from my experience in an unhappy marriage (that I thought was happy enough, for a long time), I would say to take a closer look at whether the "medical issues" are really the problem, or whether there are ultimately deeper reasons for the lack of "closeness," even if the medical issues have strained the relationship.
As for cheating, yeah, if you have to keep it secret in order to not damage your relationship, it's cheating. I say, be totally honest with yourself and others about your needs. Never put some idea of "preserving your relationship" above being honest about what you need to grow and thrive as a unique, individual person, independent of your significant other.
Thanks y'all. That's why I asked, hearing what it actually means to people is sometimes better than a dictionary definition.