Instead of a Dirt Bike (or possibly an addition to the Group Gear) should be Civilian or Military Bicycles or Mopeds.
The chance of having Horses is FAR too high given how many there are in pre-WW3 Europe as compared to the WW2 period ... Germany, for example, had around 3 million horses in 1939 and committed 600,000 to Barbarossa.
In 2000 Germany had around 450,000 horses, most of which would have died in the nuclear exchange or been slaughtered for food in the harsh winters following. I'd be surprised if a third survived the nuclear portion of the war and even more surprised if a third of those survived the immediate aftermath. So, maybe 50,000 horses in Germany in alt 2000 ... of which, proportionally by WW2 standards, 20% could be committed to military operations ... so maybe 10,000 ... and that's, I suspect, being generous as few of the Horses available are likely to be the robust breeds the German army used for logistics purposes and commiting occasional riding horses to such use would kill them off quick smart.
Other European nations have similar much smaller than WW2 horse populations (figures are easily available online).
That's enough for, IIRC, three or four WW2 style German Leg Infantry divisions or, on a similar issue basis, maybe 5-6 US Infantry Divisions reduced to effectively Brigade strength.
And, as in a WW2 German Infantry Battalion, the Horses were committed to supply duties ... there was exactly ONE riding horse, for the CO ... and they died off so quickly during Barbarossa that they were never replaced as the ones used for logistics purposes died almost as quickly.
Instead it is MUCH more likely that the PCs would have Bicycles, Mopeds or, perhaps, scavenged civilian cars (junkers) or motorcycles of all types and vintages, well and truly clapped out and kept marginally operational with spit and bailing wire.
Author: Space Opera (FGU); Rigger Black Book #1 (FASA); Orbis Mundi 2, The Marketplace, Ithura & Porthaven, Fantasy Europe (PGD); Road to Armageddon & Supplements, Displaced, Audace ad Gloriam, Farm, Forge & Steam (PGD).