Climate and Weather:

Climate is what we expect in a broader sense.... it should be warm in Spring and cold in winter etc. Weather is what we get the actual temperature of the day..... Mathematically we define climate as a long term average for that quantity (e.g. Temperature) on that day in 30 Years (say). Weather will be the value actually measured on that day. This is where the term coldest in the 50 years or a century comes from.... 

For example the Fig.1 shows the data for Mumbai:

High amount of rain in Summer is common for Mumbai. Thats the climate there (red curve) but the actual data shows that in summer of 1995 thre was a big lull in rain. Similarly in Mumbai the temperature remains the similar around the whole year at 30 deg C or above. and it is rare indeed to have temperature going below 20 deg C here, which will be called bad weather for this tropical seashore.

Effects of Ice melting:

Firstly North (Arctic) and South (Antarctic) ice will behave differently, as Arctic Ice is mainly sea ice, i.e. ice over water..... Antarctic ice on the other hand is land ice (meaning there is land below ice)... other examples of land ice are Greenland and Himalayas.....

now Sea ice what it does on melting is different from what land ice does......

Sea ice melts and lowers the sea level.... but it increases absorption of solar energy by ocean surface (ice being highly reflective)... which in turn increases evaporation ..... which in turn increases air temperature....... to the net effect is of warming...... this is the worry about the arctic ice ...... 
Also sea ice - water boundaries form the bottom water running the great ocean conveyor belt...... which actually maintains the temperatures warm in the polar regions preventing the ice age to come..... no sea ice will stop this sinking and polar and sub-polar areas will start to freeze forming more land ice and ice age will commence...... this is the worry of the North European countries and why Britain is the second highest investor in the climate change research..... 

Land Ice has the reflecting property like sea ice (i.e. that is going to be there....) but its quantity is its main factor..... this is the ice which which will contribute to the sea level on melting...... if you melt all land ice..... the sea level will rise by about 10-50 meters or more........ so the low laying lands (like Kerala coast, Maldives, Gulf coast etc.) will submerge.....