For upper-class Romans, no.

Roman social norms basically thought women should stay quiet, stay in their homes, and stay out of the way of the men. Upper-class women didn't even often eat with their husbands (or other men).

Cato the Elder (the guy who ended his speeches with "and Carthage must be destroyed!") later become Censor, a very exclusive position in charge of keeping morality in the Senate and kicking out people who were immoral. While Censor, Cato saw or heard about this Senator Manilius kissing his wife in broad daylight in front of his young daughter. Cato kicked him out of the Senate for that.

That's not to say all Romans would restrain from physical affection to their wives. It's very conceivable that lower-class Romans (or teenagers) would kiss (or do more) in public, since they had no strict etiquette rules in place.

Hello there! Plutarch (c. AD 46-c. 120) records a relevant anecdote involving the crotchety Cato the Elder (234-149 BC) and a certain Manilius he expelled from the Senate, "because he [Manilius] kissed his wife in broad daylight with his daughter looking on." But Cato then remarked, according to Plutarch, "that his wife never embraced him except when there was a great peal of thunder, and that she joked that she was a lucky man when Jupiter thundered." (Life of Cato the Elder 17.7)

Plutarch comments on the same occasion in his Moralia:

Cato expelled from the Senate a man who kissed his own wife in the presence of his daughter. This was perhaps somewhat excessive (σφοδρότερον, comparative), even if it is shameful, just as it is [for a man and woman] to welcome and love (φιλεῖν, implying displays of affection?) and kiss one another when others are present. But how is it not more shameful when those present revile and quarrel against one another, and then admonish and even find fault and speak freely in the open [about it] for all to hear, even though [a man's] private interactions and acts of kindness with his wife are to be kept hidden? (139.E-F; I tried to make a readable translation)

Curiously, some dedicatory grave inscriptions do contain open displays of affection. Robert Knapp quotes two examples in Invisible Romans (Cambridge: Harvard University Press, 2011; a good read, by the way, with somewhat iffy scholarship):

This is the gravestone Gaius Aonius Vitalis set up for Atilia Maximina, she of purest spirit, an incomparable wife, who lived with me without any quarrels for 18 years, 2 months, and 9 days, having lived 46 years, leading a life of honor and good name, my everlasting solace. Farewell. (CIL 5.3496)

Pompullius Antiochus, her husband, set up this gravestone to Caecilia Festiva, his dearest, sweet wife, hard-working and well-deserving, who lived with me 21 years without a contrary word. (CIL 9.3215)

With that, I can't speak for conditions across all of Roman history and society. I hope you find this helpful nonetheless! :)

See also: J. Bradford Churchill, "The Lucky Cato, and His Wife," Phoenix 55.1/2 (2001), 98-107.

For a slightly broader answer than the others here, the proper response is, of course, "which Romans?" There were certainly those like Cato the Elder, and while he was certainly exceptional, the fact that he existed as a general example of stern and properly Roman virtues is telling. His actions and demeanor, in other words, were attractive to a significant and influential segment of the population.

On the other hand, we must also be careful when extrapolating from someone as purposely provocative as Cato. While he was embodying traditional Roman virtues, he was also reacting against what he viewed as the degradation of those virtues, and while those people may not have been as praised by later writers they certainly existed. Most notably, the so-called "urban middle/commercial class" has sometimes been theorized to imitate certain social patterns of modern middle classes. That is, because they were not so deeply embedded within a far flung social network as the elite classes, their ideological focus was more on their immediate family than their relation to their ancestors and vague sense of familial status. Thus, when you look at funerary monuments from the first couple centuries, you see a very real focus on familial love and spousal affection. This can then be compared to works such as Satyricon, where the wealthy freedman Trimalchio and his wife, while not precisely affectionate, still set a great store on their personal relation to each other as individuals rather than as representatives of broader social networks. So we might posit that this less historically visible but still large and influential segment of the population would not have been so shy about public displays of affection.

The recent work I know of on this is Emanuel Mayer's Ancient Middle Class.