Radiation is somewhat cumulative.
Halflife isn't the be all end all measure of how dangerous the radiation is. The biggest measure is the TYPE of decay.
Alpha decay is harmless. It emits alpha particles which are essenitally helium nuclei. Alpha particles are blocked by thin surfaces like paper or your skin. Beta decay is pretty nasty though. Beta decay si from fast electrons. These can be blocked by aluminum but penetrate skin and organ tissue. They can cause damage to your DNA.
The worst however is gamma radiation. Gamma radiation goes through almost everything. It's the type of radiation that can kill you pretty quickly. Gamma radiation typically only occurs with bombs.
Plutonium 239 decays via alpha decay which is harmless. However it decays into Uranium 235 which is also radioactive. That decays via alpha decay though as well. The NEXT element is the dangerous one which decays via beta decay and a halflife of only 25 days. That means it spits out a lot of particles rather rapidly.
The thing is, the radiation you get at a bombsite isn't from leftover plutonium. it's from other stuff that got changed. For example, anywhere there is steel and radiation, you get Cobalt 60. Cobalt 60 is a deadly radioactive material with a halflife of about 5 years. Cobalt 60 is deadly because it decays by emitting a fast electron and 2 gamma rays. Standing next to Cobalt 60 is a good wya ot die a horrible painful death. Cobalt 60 is created over time in any situation when steel is sitting in an environment with long halflife materials. So, for example, if remnants of Uranium or Plutonium are hanging around, they will gradually decay and any that is near steel will create Cobalt 60. Since Uranium has a halflife of something like 700 million years, you'll get Cobalt 60 over that entire period as well.
The end result though is that you wouldn't experience big doses of radiation out in the open but rather any time you wandered next to any exposed steel.
If you want to know more about it, ask anyone who served in the US Navy on a Submarine or at any nuclear reactor. Cobalt 60 is one of those nasty things no one likes to talk about in public.