One can build such in the Mekton Technical System and Mekton Zeta Plus (which reimplements for the Zeta edition)... but it's not an obvious method. Personal scale superlight torso and 2 wheeled legs, manual controls, and a bioenergy plant, with saddle for pilot.
Skis and skates can be just personal scale wheels for the wearer, using bioenergy and pilot merge.
Likewise, one can readily abuse the Champions/Hero System vehicle rules in a similar way. Just buy additional movement with turn mode, costs endurance, and OAF bicycle. Champions 3rd lists the object def (4) and body (2).
Danger International has all three - with rules. It adds nothing to move, but gives a ×6 (instead of ×2) NCM, has DEF 2, Body 5, size ×1, uses Motorcycle skill.... but the materials list is a direct copy from Champions 3rd... with Def 4 body 2. (motorcycles likewise have similar mismatch)
HSR6 lists bicycles in the lists, no special rules
Revised Recon, a bicycle being pushed can do walking pace with up to 300lbs of cargo. Skis also have rules for overland travel.
I recall seeing Bicycle rules for CW Classic at some point, but not within the materials in the Bundle of Holding nor my collection of files from the CWIN "Car Wars Internet Newsletter" - going back a good way... '99 ish... ISTR them being HC 1, Speed by load, and not a lot of allowed load. Nor from my local copies of the once free HTML versions of ADQ.
ADQ 1-4 does have (in the Maniac solo adventure) rules for vendor push-carts... +2 to hit (all aspects), collision DM ¼, 3 DP, operator can push it to 10 mph... it also has, in the Trucking Economics Article, a reference to Combat Bicycles, which, as cargo, are 150 lb/space, and $750/space...
ADQ 9-3 has ski rules! Page 20.
Searching my PDF collection ...
- Elite: Encounters has a vehicle profile for bicycles. No skis nor skates
- FASERIP (the clone, not the original TSR) has bicycles on the vehicle speed and cost...
- Jovian Chronicles (from the bundle - 1st ed?) has entries for 1 and 2 person bikes and 1 and 2 person ebikes.
- Wraith 20th (thanks, Onyx Path for the freebie in Pandemic Lockdown) has a bicycle listed on the vehicles table. (p. 319)
- 3Deep lists bicycles as buildable light vehicles.
- Twilight 2000 1st ed has bicycle rules. (minimalistic) It has an entry on the gear table for XC skis, but no mechanics in the core. Snowmobiles and dogsled rules are in Bear's Den.
- T2K 2.2 has somewhat better on the bikes, but only the same just-a-shopping-list entry for skis.
- Aftermath has bikes, but no skis nor skates, in core.
- Albedo 2e (chessex) has a pricelist entry for bikes, no rules.
- TORG (1e) notes the tech level for bicycles, and that in the Aysle cosm, most of the UK can't remember how to operate one...
- CORPS: VDS has a bicycle as one of the worked examples... and makes provisions for vehicular skis and pontoons. Those could be applied as is to footwear.
- EABA: Stuff also uses a bicycle as a worked example. As with it's sibling, CORPS, its the extreme end of the design system.
- D6 Adventure has bicycles on the vehicle list, and in the driving rules. D6 Space only has them in the skill section.
- Mutant Year Zero has vehicle stats for bicycles, has a roller skates on a table but no rules for them.
- MYZ: Genelab Alpha has stats for "slalom gear" (skis).
- SWADE (Savage Worlds) has bicycles on the vehicle table. Annoyingly, Acrobat reader won't search it, but Windows Search does... ISTR Deluxe has them, too. Revised does not. Red Sands does...
- Warbirds has prices, but not mechanics, for bicycles. No skis/skates. Lots on planes...
- Land of Giants (for Pendragon 3rd/4th) has rules for skis.
- Blood and Treasure has minimalist rules for skis and snowshoes - avoids the movement penalty for snow.
- Hârnmaster 3 (Columbia Games) has rules for skis and snowshoes. about half a paragraphs.
- Mouse Guard uses skis as an example of a crafting in the field project...
- Rolemaster has skis on the vehicles chart in one edition. It's interesting that skis cut snow movement exhaustion by half, but require a MM roll for how far you get...
- Theatrix has an example involving a skiing chase...