Lose the idea that highs are hot and lows are cold. This is definately not always the case. For example the air around the equator is "typically" hot, unstable and often moist. Hence deep low pressure systems develop and very active storms are produced. Conversely, the air over the poles is "typically" cold, dry and very stable in other words anticyclonic.
We in the UK sometimes assume that high means warm because in the summer we are often influenced by the Azores High. As its name would suggest it originates from the Azores and drags warm air up from the sub tropics. But you will also be familiar with those beautifully clear January days when this isn't a cloud in the sky, the sun is shining, but it is bitterly cold. Those conditions are also anticyclonic - High pressure.
Try and understand how the highs and lows originally develop (normally uneven surface heating over a large area) and forget the idea that highs must be hot.
Hope this helps.