The “middle” that Joe states is relative, you could say the square hole is in the middle of the end.
Ruari, since your rim turned out to be an odd size, you might as well want to invest in a cheap new uni. For riding in snow you don’t need a splined (strong but expensive) hub, a cheaper “cotterless” one (like on your Pashley) will do. As for wheel diameter, 24", 26" and 28/29" will all work fine under snowy conditions. Depends on what you want: a bigger wheel allows for more speed, especially under more favourable conditions, but you’re somewhat more limited in technical riding. For most snow conditions in my (limited) experience a wide (e.g. 3") knobbly tyre is good, you don’t need medal studs.
If you go for the 28/29" size, you can probably order a new uni without tyre, and use the Nokian 240 you already bought. You could also re-use the seat, with UDC such custom purchases are negotiable.