Hi there
What a difficult situation for you. So, first off, I would avoid writing. It probably will cause problems. Secondly, you need to remember that quite a large number of people with dementia appear in denial that they have it. That isn't what is actually going on, their brains are preventing them from thinking logically, but your sister herself may take it as an affront, along with her hubby.
I would do two things. I would write to her GP, explaining all the circumstances, explaining that you are her twin etc. GPs are good at finding ways to broach memory issues without saying anything detrimental, he or she can find a ruse to invite your sister for a check up or something - you can suggest that to the GP in the letter. I would follow it up with a phone call to the GP after they have had time to read the letter to see what action they will be considering.
If you want fast action I think you have to come over, and then you can both talk to your sister and perhaps take her to the GP or if she doesn't want to go, make an appointment to see the GP yourself (as a temporary visitor) and then explain it. While a GP may not be able to discuss your sister with you, in terms of privacy, you can discuss your sister with him.
I think it is vital that you do get help for your sister because a) her problems could be caused by a different undiagnosed health condition which needs attention and b) the sooner she knows the sooner she can get onto a drug like Aricept, if she does have dementia, which helps slow the progress of the disease in its early stages. So my idea would be find out who her GP is, write to him, come over, visit your sister and get her to see him too. As to the husband, if he is unhelpful on this issue, then I would suggest not involving him in any way until she has a clear diagnosis.
If you are wrong and she has some other condition apart from dementia, the GP will not disclose that you have written to him/her if you ask them not to, and they can be the independent arbiter of what her symptoms mean, just make sure you clearly list all the things that seem 'wrong' to you. Having had to go behind my mother's back to do all this myself, I am glad in the end that I did, even though I was very aware that it could be seen as interfering, if it turns out to be dementia, I am afraid it is a necessary intervention. If it isn't, you may still be helping your sister's health via the back door of alerting the GP.
It may mean you have to make a trip over before January and of course travelling in the winter is no fun but if you are just going to be over there worrying about it I would have thought it would be better to take action now rather than wait. Good luck whatever you choose to do and I do hope you let us know the outcome.