Radio Times praised the story for its multi-layered structure, exploring the hidden depths in the characters. "Sarah Dollard accomplishes this beautifully in Thin Ice. She wipes away a dusting of frost to give us a window into the Doctor’s soul and examines his moral code; the ideals he aspires to and the crimes and misdemeanors he’s prepared to indulge."
The Mirror enjoyed the period nature of the show. "Any time Doctor Who dips a toe into period drama it really goes for it. It delivers a grand scale for the Frost Fair, with an army of extras, wonderful costumes, and sets filled with small touches that all come together to create a visually engaging 45 minutes."
The Telegraph, while enjoying the story, was disappointed by the ending and the effects. "Last week’s story, “Smile”, was let down by a rushed ending. The denouement here was almost as disappointing. Sutcliffe tried to blow up the ice for a reason that wasn’t entirely clear. When the creature swam off down the Thames to freedom, its strange scale and unconvincing appearance resembled a Fifties monster movie."
The Nerdist praises the work of writer Sarah Dollard. "With Thin Ice, we get the sense that she’s been able to explore the topics that are important to her, worth talking about, and don’t pull any punches. From the tackling of racism and classism to the moral dilemma of the Doctor being surrounded by death at all times and even being complicit, it’s all right there, and it’s refreshing.".
The writing was also praised by Ars Technica "The first two episodes struggled to dance between the mostly-excellent teacher/student friendship and somewhat inconsistent sci-fi plot lines. Thin Ice, however, skates through with ease. Writer Sarah Dollard—whose debut episode, Face the Raven, "killed off" Clara last season—ably steers the whole thing through a (Moby Dick)ensian world."
Digital Spy called the episode a fun romp with hidden depths. "Not only is the scenery of 'Thin Ice' visually rich, with circus folk and an elephant milling about on a frozen river, but there's also something innately odd about it. In other words, it's the perfect backdrop for one of this show's twisted trips into the past."
While Den of Geek looked at the various elements in the story. "There’s a bubbling racial and slavery subtext to the episode, and just when you think it’s going to stay there, Sarah Dollard brings it furiously to the surface."
Inverse.com looked at the relationship between The Doctor and the Companion. "Unlike more recent seasons of Doctor Who, this episode went out of its way to establish that the Last of the Time Lords himself feels like he works for the people of Earth. He calls Bill “boss” at the end of the episode and in a pivotal moment says “I serve at the pleasure of the human race.”
Screen Rant also investigated the impact of the new companion on the series. "Bill will be the first companion who is a product of Capaldi’s sometimes brusque but no less compassionate Doctor. As such, his actions at the beginning of their time together will forever shape Bill’s impression of the two-hearted alien moving forward, regardless the form he takes when it’s time to regenerate at the end of the season."
IGN looked at the structure of the story. "This third episode follows the pattern established by the previous two installments with a one-off adventure that feels in some ways like old-school Who. Here, as Bill wades deeper into the exciting insanity of the Doctor’s lifestyle, she also realizes that it’s not all fun and games and stealing pies. Ah yes, the life lessons of a companion."
AV Club admired the shift between serious and comic elements in the story. "Such sudden shifts between light and dark could undermine both aspects of the episode, but Dollard’s script is nimble enough to make keeping the audience off-balance into an asset. That can only work if the actors are confident enough in their performances to serve as an anchor for the various tones, and Capaldi and Mackie prove up to the challenge."
Finally Games Radar thinks this type of story is what Doctor Who was made for. "Unflinching storytelling at its finest, Thin Ice doesn’t shy away from the historical difficulties of taking a black companion to the 19th century. Pearl Mackie’s performance is fantastic from the get-go"
Our own review can be found in our Reviews section.