Most ice cream is not kosher for passover, but you might be able to find ice cream
with a reliable Passover hashgacha (kosher certification for passover). But if it only
has a regular year-round kosher symbol, that doesn't by itself mean that it is kosher
for passover.
(Note that while it might be possible to find ice cream that is kosher for Passover,
you cannot eat it as part of the Passover Seder meal, as ice cream is dairy and
the Seder meal contains meat. The Torah forbids Jews to mix the two.
Addendum (by another contributor):
My mother used to make ice cream during Passover.
Only if it says "Kosher for Passover".
Only if it says so on the label.
It can be if it comes from a kosher company.
No. You should eat lamb instead
Any cheeses made from kosher ingredients by a manufacturer that is certified kosher is kosher. Kosher refers to any food prepared according to the laws of kashrut (Jewish dietary laws), it is not a style of food.
Kosher ice cream can come in any flavor, there is practically a substitute for every food now a days. However, not everywhere that sells ice cream may have Kosher options. Your best bet is to ask someone who works there if they have any Kosher flavors.
It would have to be certified kosher for Passover.
The label has to say "Kosher for Passover"
Yes, only if they are specifically certified kosher for passover. You can find kosher for Passover olives at any Jewish supermarket
It can be, it would require a valid Passover hechsher.
Some Prairie Farms ice creams are certified kosher, you would have to check the package for a valid kashrut hechsher.
Yes, it can be since it is made from wine, which can be Kosher for passover if created under appropriate supervision. The bottle would require a kosher for Passover hechsher.
If you were able to find corn vinegar that is certified kosher for Passover, it would be kitniyot which means that the majority of Ashkenazi Jews would not use it.
There are kosher food companies that are now making gluten-free products Kosher for Passover and all-year-round. However, something being gluten-free has no bearing on whether or not it is Kosher or Kosher for Passover.