The business licensing requirements vary by jurisdiction. In most cases, requirements kick in progressively as revenue grows, and in many cases, you have the option to register within a certain time period AFTER the revenue exceeds that threshold. Now you're already in landscaping you say, so presumably you have already consulted an accountant and taken the proper steps with the IRS? That's the big thing... taxes.
As far as plow operations licenses and requirements... if you're operating on private property, not much applies to you. Its all the business and liability stuff you need to worry about. Basically, all you need to be "legal" is valid vehicle liability insurance and a driver's license. If you're doing commercial, it would definitely be smart to take on some additional liability insurance to protect yourself from litigation, and you should DEFINITELY consult your insurance company regarding your use of the vehicle for plowing BEFORE you decide to go through with it. There is probably some clause in your policy that says you aren't covered if you're using it for certain things commercially (even if it is already commercial policy -- it needs to be commercial for THAT USE). You ASK them what it will do to your rates SHOULD you decide to do commercial snow plowing. If the number doesn't send you running to the hills, then you can decide to do it. If the number is crazy high, shop around a bit first, but do NOT begin commercial snow plowing until you have a policy that covers you for that use. If all you have is basic personal use car insurance and you wreck something in the process of performing commercial snow plowing, your insurance company will refuse to cover you and you will be deemed to be operating the vehicle WITHOUT INSURANCE.