I have looked for the answer online, but no luck so far.
Does the ice "burn" the meat and it gets white?
How does it work?
The real question should be "what makes sausages pink" - but more later.
All meat turns greyish-white or brown when cooked. This is due to the myoglobin, which makes raw meat look pink or red, being not heat stable. When cooked it denaturates to metmyoglobin, which is grey-brown.
For pinkish sausages, curing salts are used. They contain sodium nitrite, which transforms the myoglobin to a more stable form nitrosomyoglobin, that becomes Nitrosomyochromogen when heated - and is red.
For Weisswurst, simple table salt is used in a sausage mixture that contains light coloured meats (veal, sometimes pork), fat and water, hence the whiteish-grey colour. Curing salts have a preserving effect that simple table salt does not have. Traditionally, Weisswurst was therefore supposed to eaten before noon. Modern refrigerators have made this former necessity obsolete, yet the custom remains.
According to Wikipedia, it's because of the lack of preservatives and the low cooking temperature. Veal is a light coloured meat if the calf is slaughtered at an early age and milk fed.
I don't know why you think ice is involved.
White sausages such as these contain milk powder to enhance the white color