We are going to visit Jungfraujoch in the first week of June. It has been recommended that we have hiking boots and warm jackets to keep out the wind. I would like to know if the boots and the jacket is available for rent. We would want to avoid buying the equipment as we need it only for those two days, and want to avoid carrying it throughout our trip.
Yes - it seems to be possible to rent gear. The local Swiss tourist board website gives a list of a few shops in the area (click on Explore). The first, Wyss Sport in Kleine Scheidegg offers rental of jackets and "shoes" for the trip to the Jungfraujoch - and their shop is near to the start of the Jungfraujoch Railway.
There are a few other shops listed in other towns that offer rental of boots and sticks; these might be a better bet if you are staying in one of those towns.