Yes. Strategy planning is applicable to all sizes of organization, from a single person startup to a multinational conglomerate.
Remember, a strategy is simply a communicable plan to maximize and sustain the most important objectives. So, fundamentally, the only difference between a large organization's strategy planning and a small organization's is the size of the required outcomes, which defines the scope of the initiatives. A national retailer may have an objective of $10B in revenue, which means that its initiatives must be big enough to deliver meaningfully against this. A local dry-cleaning store may have an objective of $300,000 in revenue, which means its go-to-market and other initiatives must be sufficiently sized to achieve this, and not "billion dollar ideas". This isn't to say that a small company like a local dry-cleaner can't set a much larger objective, such as controlling 20% of market share nationwide—but if such a company decides this, then its initiatives must be appropriately large in scope (and more risky).
Lastly, even if you think you don't have a strategy, you do, you just haven't formalized it, or logically and cohesively defined it. Just like when you're driving a car but not going in any specific direction, you are still driving along a route.