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Hi Neil - where is the other end of the dishwasher (ie not the pipe that connects onto the back of the appliance but the other end of this pipe) supply pipe connected ~ is it behind the appliance or under the sink?
OK you can do it this way, when you close up disconnect the pipe under the sind and drain it off, then in theory there is no water in the system to freeze.
Can you not lower the pipe under the sink to the floor?, other wise you will have to do a daisy chain connection, get a 3/4" T (with one female and two male connectors -- like this -https://www.google.co.uk/search?q=brass+3/4+y+piece&espv=2&biw=1366&bih=643&tbm=isch&imgil=IueHGI2cB1guOM%253A%253BKFiws4RpPBshmM%253Bhttps%25253A%25252F%25252Fwww.amazon.co.uk%25252FWassertechnik-571339-Brass-Y-Piece-inch%25252Fdp%25252FB001051NG4&source=iu&pf=m&fir=IueHGI2cB1guOM%253A%252CKFiws4RpPBshmM%252C_&usg=__sx7gFxcj7SXSVDaBI7RRdvA6qho%3D&ved=0ahUKEwjRr8em7unNAhVHHxoKHUEUDaEQyjcIcQ&ei=9cCCV5HhHce-aMGotIgK#imgrc=IueHGI2cB1guOM%3A) connect that to the back of the dishwasher and then connect the hose from the sink to the dishwasher then other side of the T connects to the washing machine supply hose.
Nothing you can do about that there is no drain off for a dishwasher pump, however I have never seen a dishwasher pump freeze up because it is connected to rubber pipes that can expand whereas the plastic inlet valve casing can't.