The frost will kill the flowers so not much point in trying to stop the water from freezing. Best to use winter flowering plants in a pot like primrose or hyacinths.
How about getting something hardier like ferns or holly or even a dried or fake arrangement which will last longer?
I was sent a lovely bouquet the other day which had some holly and fake little berrylike flowers covered in a frosting like snow, beautifully Christmassy and they are really lasting.
Not very practical at the graveside but running the stems under warm water while cutting them diagonally can make them last longer.
Just had another though, how about a hot drink warmer which is battery operated, like a coaster which stays warm to keep the drink warm. It could be put under the glass and covered somehow?
You could also try using something insulated as a vase though you'd have a certain amount of heat escape at the top but you could try minimising the escape by sealing the top with the flowers or similar.
thanks for your answers, the pots are actually within the gravestone as plants and wreaths arent allowed on the actual "plot" as it needs to be kept clear, so the only thing i can do it put something in the water.
at this yime of year i put pieces of verigated shrubs, holly ,and pieces of bushes with berries on out of the garden on my mums grave as they dont seem to mind the water freezing over and last quite well if you want a bit of colour buy a few artifical ones to brighten it up