Usually, philosophers explain the meaning and truth value of counterfactual statements using possible world semantics. However, that approach requires one to accept the existence of possible worlds. Now, a disbeliever of possible worlds can simply bite the bullet and accept that, for example, counterfactual statements like "Unicorns could have evolved on Earth" and "I could have gone to the gym instead of writing this question" are, strictly speaking, false, even if they are useful in daily life. However, is there a middle way between these two extremes, such that statements like "Unicorns could have evolved on Earth" have meaning and a truth value, but do not require the ontological extravagance of the existence of possible worlds? And have any philosophers talked about and came up with a solution to this problem?
There are a few things that can be said in answer to this question.
As has been pointed out in the comments, one does not need to believe that possible worlds have real existence in order to make use of them. Possible world semantics has proved highly useful, and not just for understanding counterfactuals, and many of the people who employ possible worlds think of them merely as information states or situations or scenarios. David Lewis is a realist about possible worlds, but he is in a minority in that view.
Not all accounts of counterfactuals make reference to possible worlds. One of the earliest attempts at a theory of counterfactuals, that of Nelson Goodman, regards them as propositions deduced from laws of nature. This is pretty implausible as it stands, since many counterfactuals have little or nothing to do with laws of nature. If I say, "If Fred had insulted me once more I would have punched him," this does not mean that my punching Fred is somehow deducible from laws of nature. For one thing, human behaviour is not that predictable, and for another that would be confusing the meaning of the conditional with the reason for accepting it. Also, we may wish to express counterfactuals that speak of universes with different laws of nature, or even different logics.
Other accounts treat counterfactuals as propositions that taken together with additional cotenable assumptions permit deduction of the consequent, e.g. Frank Veltman. Others again treat counterfactuals probabilistically, e.g. Ernest Adams and Dorothy Edgington. Some probabilistic accounts use possible worlds to define the sample space, so possible worlds can still creep back in, but they are not essential. Some accounts, e.g. that of Judea Pearl, specifically use Bayesian nets to understand counterfactuals in terms of interventions.
It is worth noting that not all theorists about conditionals treat them as having truth conditions. Some prefer to understand them in terms of assertability conditions. This view is particularly associated with Adams and Edgington. Also, many accounts treat counterfactuals as context-dependent, so it is not simple and straightforward to state under what conditions they hold.
The answer is trivially yes. In any case, as other commenters have...erm, commented, possible worlds terminology is metaphoric, and only an idiot, or an exceptionally clever philosopher such as David Lewis, would take it literally.
To take your example regarding unicorns...
To begin with, let us suppose that by 'unicorn' you mean a horse with a horn. That is, we are disregarding magical properties, pink fur, twinkly stars, the ability to utter phrases about the destiny of a chosen one, or any of the other nonsense that might be associated with unicorns by children susceptible to the marketing ploys of exploitative corporations such as Disney.
Whether unicorns could have evolved on Earth depends upon what version of Earth you have in mind. If you mean Earth populated by all the other life it has today, then one might simply argue that unicorns could not have evolved, on the grounds that if they could have they would have, and since they didn't ergo they couldn't have. Or you could take the view that horses obviously did evolve, as did other animals with a central horn, therefore it is not out of the question that a horned horse could have evolved had certain selection pressures existed. If you had any sense of intellectual rigour, you might feel obliged to bolster your claim by outlining the sorts of selection pressures that might have caused a long twisted horn to evolve from a more rudimentary bump on the head of some initial horse that began the evolutionary line through a random mutation, and you might marshal some form of argument about comparable dna structures in horses and rhinos, narwhals etc etc. Either way, you can leave aside all of the jargon about possible worlds and still have a meaningful discussion about truth values.