Yes a bucket of a mixture of small ice pellets, say a few millimeter size, plus water, (this bucket being enveloped with some insulation) would be a great zero degrees Celsius reference point.
… “the actual melting point of ice is very slightly (less than a thousandth of a degree) below 0 °C.” …
isotopic distribution of heavy and light elements in water also has a very slight effect on melting point. So, rainwater and water distilled from ocean will not melt at the (exact) same temperature.
Now, about small particle fusing together this is true not only of ice but of any material.
it’s called sinteringand it is caused by diffusion and a lowering of the surface energy.
This process is faster when the material is near it’s melting temperature and faster yet if in contact with any miscible liquid phase.