Does freedom of speech apply to government officials?

Recently, Rolling Stone caused a furor by putting accused Boston Marathon bomber Dzhokhar Tsarnaev on the cover. In response, Boston Mayor Thomas M. Menino wrote to the publisher of Rolling Stone, telling him that doing so “rewards a terrorist with celebrity treatment” -- treatment the magazine should have given to the survivors. Other government officials were similarly critical of Rolling Stone. My first reaction was that these government officials had no place saying anything about a publication. But then I wondered: Doesn't the First Amendment still apply to them? In other words, do government officials have freedom of speech?

See: http://bostonherald.com/news_opinion/local_coverage/2013/07/mayor_top_cop_blast_rolling_stone_over_tsarnaev_cover
And: http://www.rollingstone.com/culture/news/jahars-world-20130717