We just published a newly-overhauled set of lawn care web pages (accessible via the link), which include information about zoysia care. Zoysia is still dormant (as you noted, it'll look straw-like), but early-season weeds like wild onion/garlic (it looks like a taller grass but definitely smells like onion/garlic if you crush its leaves) and any stray cool-season turfgrass or weedy grass types (tall fescue that seeded in, or the weedy Roughstalk Bluegrass) might be greening-up and in active growth now. Generally, though, zoysia lawns in good condition don't have many weed problems, and especially don't tend to need pre-emergent herbicide put down in spring.

Weed-and-feed products combine pre-emergent herbicide with fertilizer. We do not recommend their use on any lawn type, for several reasons. Instead, fertilize as the application chart notes for zoysia (it's much too early to apply fertilizer to zoysia now), and identify any weeds present to learn how best to control them, which may involve different tactics depending on which species they are. If you don't recognize the weeds, feel free to share photos of them here and we'll try to ID them. Many species of lawn weeds actively growing and flowering now will die on their own by the end of spring without needing treatment.

You can find dethatching information (plus aeration, irrigation, fertilization, etc.) in the Maintaining an Established Lawn page, and seasonal zoysia-specific care steps in the Lawn Maintenance Calendar page.

Miri