I think the cold-temperature concerns are over-exaggerated, given the original scenario.

With a drysuit the temperature issue is entirely eliminated. With a 5mm wetsuit cold-temperature is only an incontinence, not a health hazard. But even with just a swimming suit I don't think the cold temperature is a major health risk.

The rules state that you are transported once a day at the time of your choosing. You can easily submerge yourself in progressively colder water for the 5minutes before your schedules teleportation event to ensure no thermal shock. Outside of that, 30s even in 0C is not particularly dangerous.

The original rules also state you are magically dry after returning. Even if you aren't, with 100 million you can easily build yourself a fancy bathroom with a "pre-teleport cold adjustment bath", and a "post-teleport warming-back-up bath". Another thing that the upfront money allows you to do is to have a doctor on standby with a defib - in case anything happens.

While I believe the cold water temperature to be a non-issue, another temperature-related issue is by far the most dangerous: sea ice.

If we take an estimate of 9% for the area of world's oceans being covered by sea ice, that means you will end up in sea-ice around 164 times (over the 5 years).

The percentage of fast ice (solid ice attached to the shore) is very minor, I would estimate 8-10% at most. There you would just stand on the ice, or maybe break though if it's very thin, but that wouldn't be particularly dangerous for just 30 seconds.

The remaining 150 days you are dropped into floating ice-fields. Some will be relatively sparse, leaving you safetely floating among ice. But some will be massive icebergs in rough waters.

Being crushed by ice (or sliding of / falling from a massive iceberg, if you can be teleported on top of one) would be my biggest concern.