There is no IE10 on XBox. It is based on IE9, so in theory if your site works in IE9 desktop it should work fairly well on the XBox, except for adaptations that need to be made to display well on a screen you interact with from distance with alternative input methods.
You can find the IE for XBox developer’s guide at http://www.microsoft.com/en-us/download/details.aspx?id=30442
You should only detect the User Agent string as a last resort. The UA strings for IE for XBox are:
- Desktop mode: Mozilla/5.0 (compatible; MSIE 9.0; Windows NT 6.1; Trident/5.0; Xbox)
- Mobile mode: Mozilla/5.0 (compatible; MSIE 9.0; Windows Phone OS 7.5; Trident/5.0; IEMobile/9.0; Xbox)
The regular UA string is desktop mode. A user can switch to mobile mode if they have a SD TV and the web page would work better if given the mobile version. The key token to detect is "Xbox".