my t and i talked for a bit on christmas eve just to say hi to each other and that we were thinking about each other/ etc. it helped a lot as we hadnt had time to talk for a about ten days. she really wants to come home. christmas makes her home sick. i told her i have money stashed away to buy her plane ticket whenever she is ready

Oh and on christmas morning we also texted t a christmas message.
like someone else said i dont think an email to wish your happy christmas. they dont have to respond, or check their email until they have time, so its fairly non intrusive.