Why don't you want to specify the format provider?
If it is just laziness then I can recommend defining two snippets. ic for CultureInfo.InvariantCulture and cc for CultureInfo.CurrentCulture.
Never assume anything about how conversion to string works with the default culture. Not everyone in the world uses the gregorian calendar. Some day you customer might hire a contractor with a computer with another calendar as default and then you are not generating correct XML. Explain then to your customer that you didn't want to follow the FxCop recommendation.
Best thing would be if .Net included a Xml Culture. Then you could just do
DateTime.Today.ToString("d", CultureInfo.Xml)
For some reason Microsoft choose to create a separate class instead XmlConvert. The class has been there since .Net 1.0.
XmlConvert.ToString(DateTime.Today, "yyyy-MM-dd")
will always create a correct Xml date.
Not sure if it is bug or intended behaviour but XmlConvert.ToString(DateTime.Today, "d")
will not create a valid Xml date.