A river or a sheet of ice that lasts all year and flows. With progressive burial, the points melt away, and the snow becomes granular and packs together. During this process, ice melts where it is being squeezed most, and the water moves to places where pressure is less and resolidifies. This means that the atoms rearrange into new ice crystals, and you have solid ice which, internally, is composed of a mosaic of crystals that fit together tightly. This recrystallized ice forms only when the ice has been buried by 10s of meters.
Glaciers are able to flow, though they are solid.
This happens in two ways. Eventually, this ice starts flowing downslope due to gravity. It's just that the position of the toe is retreating, because ice is melting away faster than it is supplied from above. Ice builds into a thick mound several hundred meters thick. Then, because ice is a weak material, the weight of the ice itself causes the mound to spread laterally, forming a broad ice sheet, and the toe migrates to lower latitudes.