Do prizewinners use prize money for academic purposes?

I suspect awardees do not use the award money to do research in the majority of instances. My opinion is not judgemental: in most cases, it would not make much sense to spend that money for research purpose.

In fact, the average Nobel (or Fundamental Physics Prize, probably the largest sum awarded as prize to scientists) is shared among several people, and amounts to a few hundred of thousands of US dollars each. While that is a large sum for personal purpose, it is not necessarily a large sum for research purpose.

More importantly, a Nobel medalist is certainly in the league, and with much better prospects of success, to obtain research grants that range in the millions (European research council grant for example). If you can fetch millions of research money every 5 - 10 years, what difference your ten times smaller, once-in-a lifetime Nobel prize sum would make? Of course the argument above is even stronger for the Fields medal, given its relatively low monetary value.

Other have noted that it depends upon the Award. In the case of MacArthur "Genius Grants", popular press articles have examined how recipients spend this prize.

This New York Times article describes how most recipients used the money for things such as their charities, own research, debts, and other causes.

This Time article examined how 6 recipients used their prizes.

Unless there is a particular criterion requiring that the money be spent on research causes, there is generally no restriction on how the prizewinner spends the money. It could certainly be used for things like travel on sabbaticals, donations to charitable causes they support, or even personal expenditures.