People usually do not use です・ます when talking to themselves. So that would rule out thinking out loud, anyway.
It’s going to be hard to explain why this isn’t something someone would say to another person about their own search. A native I checked with said, ~といいんですけど would be more natural for their own search, but I don’t have a full explanation of why that’s more natural than yours.
As @Leebo indicated, the fact です is used here is a hint that it’s a suggestion to another person, rather than one’s own thoughts. Additionally, you’d expect to see な, がな, けど, or something other than ね if it were one’s thoughts. Without seeing the context I can’t say for sure, but I’m reasonably confident this is one person suggesting another find a good fridge.
That being said, I might translate this, “I hope you find a good fridge,” or “I wish that you would find a good fridge.” Adding ね kind of softens the suggestion.
I believe “would find” is subjunctive mood in English. I also think the ですね at the end does indeed imply speaking to someone else, but the softening to my mind is due to the inquisitive nature of basically asking for a head nod.
Dunno if it’s technically correct, but to my ear, “It would be good to find a nice freezer, wouldn’t it?” would be a reasonable translation. It covers the tone, the subjunctive/wishful nature, and the softened inquisitive seeking for agreement at the end.
If it’s not correct (definitely possible) I’d like to know why so I can correct my own understanding.
I mean, without knowing the context of the sentence, it’s hard for us to narrow it down too much further than the general ballpark we’re already in. The reason I leaned more toward what I offered is because といい paired with a volitional action is generally used to make suggestions or to give advice, but adding ね is intended to soften the tone to make it less direct. Translating ね as “wouldn’t it?” is a little too literal, as that kind of implies the outcome is perhaps uncertain, and that disagrees with the と conditional. と indicates a natural consequence that is always expected (unlike たら and ば). It doesn’t necessarily have to be 100%, but it doesn’t leave much room for doubt, either. Consequently, ね has less of the sense of asking for confirmation or agreement in this context.
Rather than meaning “right? isn’t it?” here, ね is behaving more like it does in てね, where it’s used to soften a request or demand. You wouldn’t translate ね as “right?” in this case. Instead, it’s more like, “OK?” or “all right?” Compare, “do your homework” (very direct), and “do your homework, OK?” (softer in tone). That’s closer to the sense when you use it with といい, but even then it’s not quite the same feeling. といい…ね is really more used to express a wish or hope for a good outcome for someone. Sometimes it can be suggestive in tone, though.