JPL Horizons has some trajectory information for Snoopy, but it cannot be used to determine where Snoopy is today. However, it may be of interest to see what Snoopy's orbit originally looked like.
From the Snoopy body data file:
Launched: May 18, 1969 @ 16:49 GMT/UTC from Kennedy Space Center, USA
The Lunar Module (LM), whose later ascent-stage post-jettison trajectory is represented here, came within 14.4 km of the lunar surface (May 22 @ 21:30:43 GMT/UTC), the point where the powered descent to the lunar surface would have begun for an actual landing.
During autonomous lunar orbit operations, and after closest approach, the LM then jettisoned its descent stage at a selenocentric altitude of 58.2 km. Because the crewed LM ascent stage was not launched from the Moon's surface, docking with the Command Service Module (CSM) in lunar orbit was achieved with considerable propellant remaining on the LM. After docking and crew transfer from the LM to CSM, the LM was jettisoned and the surplus propellant expended in ground-commanded separation and depletion burns, ultimately departing the Earth-Moon space with a heliocentric trajectory estimated here.
SPACECRAFT TRAJECTORY: The trajectory here is a reconstruction of the Apollo 10 Lunar Module ascent stage ("Snoopy") departure trajectory developed by Daniel R. Adamo under contract to NASA in 2012. The trajectory spans the time interval from 1969-May-23 05:38 to May 28 @ 00:06 (GMT/UTC).
To extrapolate to future times, the following heliocentric IAU76 J2000 ecliptic osculating elements can be manually input into Horizons as starting conditions for a ballistic numerical integration using the telnet or e-mail interfaces:
EPOCH= 2440369.50 ! A.D. 1969-May-28 00:00:00.0 (TDB)
W = 4.378387492993282E+01
EPOCH Epoch Julian Day Number, Barycentric Dynamical Time
EC Eccentricity, e
QR Periapsis distance, q (au)
IN Inclination w.r.t xy-plane, i (degrees)
OM Longitude of Ascending Node, OMEGA, (degrees)
W Argument of Perifocus, w (degrees)
Tp Time of periapsis (Julian Day Number)
Uncertainties and errors in the extrapolated position prediction will increase as the time from the EPOCH increases. Predictions for this man-made object years past the EPOCH are problematic due to unmodeled-but-cumulative solar pressure and out-gassing accelerations, yet no further tracking data to characterize the forces.
The Sidereal orbit period is 338.06588 days, and the semi-major axis is 0.9497339 AU.
As mentioned, we can feed those orbit elements to Horizons to get trajectory data. The results should be reasonably accurate for the first year or so after the epoch, but they will certainly not be correct for the present era.
FWIW, here's a Horizons query for Snoopy that covers the timespan given above.
Here's a heliocentric plot of Snoopy (red), the Earth (blue), and Venus (green) from 1969-May-24 to 1970-May-24, using a time step of 7 days. The numbers on the orbits are plotted every 4 weeks. The horizontal line from the Sun is the equinox line. We're looking down onto the ecliptic plane, from the north. Snoopy's orbit is (was) only very slightly inclined from the ecliptic plane.
That plot was created using a version of my 3D orbit plotting script, originally posted on Astronomy.SE. Here's the modified version, which contains the orbital elements for Snoopy. To specify the Snoopy elements as a target, use a semicolon
;. Please see the Astronomy.SE post for further info on using the script.