The reactor pictured is a research 'pool' reactor. These are not power reactors, but are designed for study of nuclear reactions or for small scale manufacture of special isotopes (e.g. Molybdenum-99 which is a vital medical isotope, for which the only practical source is this type of reactor).
The purpose of the water in a 'pool' reactor is twofold. First, to keep the fuel cool, 2nd to act as a radiation shield to protect staff working above it.
The advantage of using a thick layer of water (about 30 feet) is that it's cheap, simple to maintain, inherently safe and makes servicing and fueling the reactor very simple.
Chances are that the water isn't particularly hot, as the reactor power is such a reactor is low, and they rarely operate for prolonged periods.
So, if you swam in the surface water, you probably would get a small radiation exposure only - the bulk of the water would still be providing shielding. Obviously, if you dived down, then the radiation exposure would increase exponentially. The water may, however, be contaminated with trace amounts of heavy water (not radioactive, but minimally toxic- due to the different chemical properties of deuterium, compared to hydrogen) and tritiated-water (radioactive). Contamination of the water by other isotopes would be unlikely, as the nuclear fuel (weapons-grade, or near weapons-grade uranium) is tightly enclosed in sealed metal rods.
Falling into the reactor pool is a recognised hazard when working around this type of reactor. So, you do sometimes see life preservers at the side of the pool in photos.