Which tool is most suitable for cutting thick cardboard with ease?
My preferred tool for heavy card is the classic Stanley 99 knife.  The blade is slightly stiffer than those of the snap-off craft knives, and the metal handle is good and solid.

If you do go for a snap-off knife, for heavy card stick to one that takes 18&nbsp;mm or even the rare 25&nbsp;mm blades, rather than 9&nbsp;mm blades, which are too flexible (but great for finer work on thin card).  The cheapest of these 18&nbsp;mm and 9&nbsp;mm knives are rather flimsy and don't latch very well, so it's worth buying a good one (probably sold singly rather than in a big pack).

You should buy plenty of blades, as card can blunt them fairly quickly and a blunt blade tears the workpiece more easily than a new blade.