Not at ice divides (like hydrological divides) where ice cores are taken (ice cores are almost always taken at divides because the ice flows apart, so the stratigraphy is not as disturbed). It's too cold to melt out there anytime soon. These are high-elevation locations, so there is either no melting (East Antartica ones ~3000 m) or extremely minimal melting, rarely, during the height of summer (Greenland and some other places in Antarctica). In Antarctica, surface melt is a rounding error everywhere, and response to climate change is almost entirely due to ice sheet-ocean interactions with a warming ocean and changing currents, and a thing called the marine ice-sheet instability.

At any rate, these locations will always be accumulation zones where more snow falls then melts (with the mass balance preserved by diverging flow so as to continuously thin the ice, to approximately compensate), with melt events occuring only rarely. The concern there is that meltwater could contaminate near-surface compacted snow (firn) layers, but even then it wouldn't be enough to do much. As such, stratigraphy will be reasonably preserved even if the ice sheet as a whole draws down significantly (including at divides).

Really extreme climate change (which is in the cards long-term) could eventually change this, especially if the ice sheets reduce enough in height such that a significant ice sheet-elevation feetback occurs. However, we'd have much bigger things to worry about at that point.

We have the most extensive data available for recent years, though. Ice core samples are also nothing new, they've been extensively studied for decades. Many of these cores are carefully removed and placed in ice cold storage warehouses: https://qz.com/1590747/an-antarctic-ice-core-may-show-1-5-mi...