Is it green/grassy in march?

I'm planning on visiting Tokyo and Osaka in early March. I wanted to know if it becomes green and flowers start blooming again. Because everything seems so bare and dry in winter. All the sights look so pretty because of the gardens and I don't want to visit dry gardens :(

It depends when you come in March. In Osaka, the weather is typically warmer than it is in Tokyo, so it doesn't really snow in Osaka. You'll definitely be able to see it much greener than compared to Tokyo. However, do keep in mind that it depends on the weather. Usually by end of March into early April, it starts to warm up again and the weather gets very nice.

I don't want to visit dry gardens :(
Dry gardens are one of the cultural highlights in some places - notably Ryoanji in Kyoto as a famous example. I have a group coming in July who have specifically requested a day in Kyoto visiting a temple complex that features several dry gardens. (I am also reminded on some rock gardens in Sapporo that are very beautiful.)
Winter time some of the grasses do die-off and go brown, but the come away again in spring, and many of the trees are ever-green (cedar/sugi for instance). Pines are a favourite in Japanese art and history/culture because they are green year round.
When I think about the gardens and places I visit through March they feature greenery, grass and the new spring growth - plum tree grove at Nijo castle as an example. Lots of greenery, but of course, too early for things like summer flowers - they are summer after all.

As a rule of thumb: vegetation stays barren until the cherry blossom season, and it becomes green again from around the end of the cherry blossom season. So, no, most vegetation is still barren in March in pretty much all of Japan except the southern islands.