Not only does this depend on what your lease states as Laura said, but it can also depend on what type of rental you are in (an apartment, duplex, or a single family house) and it can depend on what state you are in.
In OH, the LL is never responsible for snow removal. However, the tenant can be made responsible for this by lease clause as part of the required yard maintenance.
In some states, the LL can be responsible for snow removal for multi-family housing (apt. complexes), but not for side by side duplexes or single family houses with no shared walks.
You really need to post more info before anyone can answer this.