The short answer is YES, but with a very important caveat. It won't be colder than usual, but colder than it would have been if the Greenland ice sheet weren't there to absorb that heat, and by a very small amount.
This is true for the mean global temperature, but when it comes to the actual strength of one winter season in a particular location, the atmospheric patterns play a much bigger role than the melting of ice sheets.
The latent heat (i.e. Enthalpy of fusion) of water is huge. The amount of energy needed to turn 0°C ice into 0°C water is the same as the amount required to heat up 0°C water to 80°C. Therefore, ice sheets and glaciers have a buffer effect on climate, as they are able to absorb a large amounts of energy without an increase in temperature.
Figure: Temperature curve of water as heat is added to 18g of water.
Despite of that, it is still a very small amount on the overall energy budget of the Earth, let's do the math:
280 Gt/year = 2.8e17 g/year
Latent heat = 333.55 J/g = 0.09 Wh/g
Total latetent heat = 2.8e17 g/year * 0.09 Wh/g = 2.5e16 Wh/year
That means a energy flux of 2.5e16/(365*24) = 2.8e12 W
Earth surface = 5.1e14 m²
Equivalent radiative forcing = 2.8e12/5.1e14 = 0.006 W/m²
Which is very small, in fact about a 0.4% of the radiative forcing associated to CO2 (see figure below):
The problem is that the resulting water have a impact in sea level rise and seawater salinity, that can in turn have an effect on ocean currents, deep water formation and other phenomena that can change the heat redistribution on earth. On the other hand, the reduction of ice sheets increase the albedo (because the bare ground absorb more energy than snow or ice), so that at the end the Earth will capture more energy leading to a positive feedback. Also, as the ice sheets get thinner, they will receive less snow (and more rain), therefore enhancing further reduction of the ice mass.
Finally, I have to add that when it comes to ice sheet models and climate models, the latent heat is always taken into account and if there were no latent heat, the figure for anual ice loss would be much bigger than 280 Gt.