Photoswitchable, ambipolar field-effect transistors (FETs) are fabricated with dense networks of polymer-sorted, semiconducting single-walled carbon nanotubes (SWCNTs) in top-gate geometry with photochromic molecules mixed in the polymer matrix of the gate dielectric. Both hole and electron transport are strongly affected by the presence of spiropyran and its photoisomer merocyanine. A strong and persistent reduction of charge carrier mobilities and thus drain currents upon UV illumination (photoisomerization) and its recovery by annealing give these SWCNT transistors the basic properties of optical memory devices. Temperature-dependent mobility measurements and density functional theory calculations indicate scattering of charge carriers by the large dipoles of the merocyanine molecules and electron trapping by protonated merocyanine as the underlying mechanism. The direct dependence of carrier mobility on UV exposure is employed to pattern high- and low-resistance areas within the FET channel and thus to guide charge transport through the nanotube network along predefined paths with micrometer resolution. Near-infrared electroluminescence imaging enables the direct visualization of such patterned current pathways with good contrast. Elaborate mobility and thus current density patterns can be created by local optical switching, visualized and erased again by reverse isomerization through heating.