Physical change: a little bit of the ice melts, thus the proportion of ice mass to water mass increases. Temperature does not change. Entropy increases because heat was added to the system (refer to example no. 1 and 2). Because this entropy increase is accompanied by an increase of liquid at the cost of solid, we conclude that entropy of solids is lower than entropy of liquids.
If a tiny amount of heat is withdrawn, entropy decreases and you get more ice and less water. Temperature stays constant, of course.
Closed system, if the heat supplied or withdrawn is substantial. Isolated system, if the respective quantities are really very very tiny, about the order of magnitude of statistical fluctuations.