Wow, I should have written this up a while ago when I had the idea myself. But Snoopy is so small (it's just the ascent stage) and it's in a volume of space so huge that the chances of seeing it seem pretty small.
There are quite a few Saturn V S-IVB stages in solar orbit (those from Apollos 8, 9, 10, 11 and 12) that are quite a bit larger and brighter than Snoopy. But I don't know of any that have ever been rediscovered with the probable exception of the Apollo 12 stage when it was temporarily recaptured into earth orbit in 2002.
Anybody know if any Apollo service modules survived? I think most of them burned up while their command modules re-entered, but at least one (Apollo 11) had been intended to 'skip' off the atmosphere and enter a solar orbit. Did any actually do that?
This would only be possible for service modules returning from the moon, as only they have enough energy to enter solar orbit. Apollo service modules used on earth orbital missions necessarily burn up because their service propulsion system engines are used to perform the retro maneuver.
I don't even know how to find Snoopy. We can start with its last known state vector and integrate to now, but after 43 years any initially small errors would result in huge uncertainties in its present position. Especially if, as seems likely, it has already made several close passes to earth.
It is difficult to model every force that acts on an object in space. The gravity of the sun, planets and their moons is the least of our problems. One of the biggest unknowns is solar photon radiation pressure. The forces may seem small, but because they're continuous they add up over time. Computing it depends not only on having a detailed spacecraft physical model (which we have) but also on its attitude with respect to the sun (which we don't have).
And there could be other forces we can't model, such as cabin venting, inevitable leaks from pressurized tanks and the like.
Snoopy would have to come very close to earth (considering the uncertainties) for us to see it given its very small size. Our best chance would be optical, as the brightness of a sunlit object at relatively constant distance from the sun varies as 1/r2 from the observer.
Radar would probably be impractical because of its 1/r4 law. There are large radars that can see deep into space, but they overcome the 1/r4 law with very high gain and therefore narrow beam antennas that require very accurate a priori knowledge of position. It's impractical to search a large region of deep space with a radar. The space surveillance radar "fence" in the southern US that does most of the work of updating the NORAD catalog can only see objects in near earth orbit.