Is running a nightly job that updates the statistics way too much? Can that affect the system's performance?
It depends. How long does a nightly update take? Is the update happening at a slow query period/ is auto create statistics still enabled?
Each database has two options related to statistics: auto create statistics and auto update statistics. Typically, both should be left enabled for databases. Statistics are automatically updated when certain thresholds within SQL Server are met (e.g a percentage of row changes that the stat was based on). Once the threshold is reached, SQL Server will automatically update the statistic(s) defined in the table.
If your maintenance window allows it you should certainly update statistics nightly since the auto update system is certainly not perfect.