This paper presents the findings of an exploratory study on the continuously generating Big Data on Twitter related to the sharing of information, news, views, opinions, ideas, knowledge, feedback, and experiences about the COVID-19 pandemic, with a specific focus on the Omicron variant, which is the globally dominant variant of SARS-CoV-2 at this time. A total of 12028 tweets about the Omicron variant were studied, and the specific characteristics of tweets that were analyzed include - sentiment, language, source, type, and embedded URLs. The findings of this study are manifold. First, from sentiment analysis, it was observed that 50.5% of tweets had the ‘neutral’ emotion. The other emotions - ‘bad’, ‘good’, ‘terrible’, and ‘great’ were found in 15.6%, 14.0%, 12.5%, and 7.5% of the tweets, respectively. Second, the findings of language interpretation showed that 65.9% of the tweets were posted in English. It was followed by Spanish or Castillian, French, Italian, Japanese, and other languages, which were found in 10.5%, 5.1%, 3.3%, 2.5%, and <2% of the tweets, respectively. Third, the findings from source tracking showed that “Twitter for Android” was associated with 35.2% of tweets. It was followed by “Twitter Web App”, “Twitter for iPhone”, “Twitter for iPad”, “TweetDeck”, and all other sources that accounted for 29.2%, 25.8%, 3.8%, 1.6%, and <1% of the tweets, respectively. Fourth, studying the type of tweets revealed that retweets accounted for 60.8% of the tweets, it was followed by original tweets and replies that accounted for 19.8% and 19.4% of the tweets, respectively. Fifth, in terms of embedded URL analysis, the most common domains embedded in the tweets were found to be twitter.com, which was followed by biorxiv.org, nature.com, wapo.st, nzherald.co.nz, recvprofits.com, science.org, and other URLs. Finally, to support similar research and development in this field centered around the analysis of tweets, we have developed an open-access Twitter dataset that comprises tweets about the SARS-CoV-2 omicron variant since the first detected case of this variant on November 24, 2021.