This is a great question. It's hard to measure something like fear - especially when it is felt in its various degrees by the hundreds of thousands who arrived "As the World Rushed In" - as J. S. Holliday titled his classic book on the 1849 California Gold Rush. I have edited two major works on the Gold Rush - both written by young men (two brothers writing home and one 49er keeping a journal); they arrived and then spent their lives in the West, and I'm not sure how to answer your question even for these three examples who I know very well. They documented the beginning of their journeys - both with the journal on the day of departure and with the brothers writing letters to home in Pennsylvania from the port on the East Coast
First of all, most - but not all - of the 49ers were young men. I once wore a younger man's clothes and I remember being immortal. I had a sense of what fear was, but not as I learned to appreciate the concept later in life. It is why the young are sent to war - they all know they will survive even though not all of them do.
The young 49ers I have come to know were far more excited than fearful, but I do not know how much they were covering up - how much of the excitement was bluster when they were actually terrified. And terrified they should have been. These two sources are not unique in the way that they documented the deaths of compatriots. Death stalked the 49ers - on the trip to the West and then once they arrived. The two brothers who wrote home would both be dead in eight years, one dying of an infection from striking his foot with a pick and the other a few weeks later from exposure to winter's cold. Life was hard everywhere, but unique, harsh challenges faced those who ventured to the Gold Country to try their luck.
This isn't much of an answer. All I can provide are impressions. I suspect there was a good amount of fear, but those who forged ahead masked it - for those around them but also for themselves, using the excitement of the possibilities to disguise the trepidation that could only have been natural.
Americans traveling west into the frontier always contained a bit of danger dating back to well before the revolution and miners of any stripe were no different. There were also many different western gold rushes over the course of the 19th Century. While I've read a few books on them, I'm going to speak of a more specific case which I found in my research that I think might be a reasonable example of what a typical young gold seeker might have felt.
First I want to apologize for not having the specifics on the source here, I did this research nearly 25 years ago and have been unable to find my notes. The story at the time resonated with me as I was nearly of age with the protagonist when events occurred in their life. The source is from a family (not mine) journal from some original Homesteading family in central Kansas that I read in doing some research on what the post-civil war homesteading life was like.
The story starts with a semi-literate boy of around 14 (+/-maybe 2 years the dob is a bit vague in the book) living in Ireland in 1857. His mother had passed from a coughing sickness (TB? Cancer? not really sure just labeled as a coughing sickness) when the boy was just old enough to start helping his father in the field. At some point in 1858, his father got in trouble with the law (debtor's prison or some such, didn't specify just said he was jailed) and the boy's aunt and uncle (mother's side) took him in but then packed him off to New York possibly to find work with his uncle (father's brother).
He arrived in New York with his clothes on his back and some odd bit of loose change that he managed to "find" on the ship. He had no luck finding his uncle and begged (possibly stole) and worked odd jobs (including hawking newspapers, again possibly stolen) to live on.
He was hawking newspapers when word spread of the finding of Gold in Colorado. Having no real sense of geography, little money, but a dream and some street sense, he decided he could make it rich in Colorado so he managed to sneak on to a west-bound train only to get kicked off somewhere in Pennsylvania. He continued train hopping and working odd farm jobs across the midwest for some time until he finally fell in with a group of young men heading out from Kansas City and Lawerence heading over a dubious route toward Denver. They ventured off the Sante Fe Trail somewhere West of Fort Riley with some horses that were of poor quality, some of which might also have been stolen. When one of the said horses died near the homestead of the aforementioned family, our young man is forced out of the group as he is the youngest, the poorest, and possibly the only Irish in the small band.
He makes his way to the dugout of the homesteading family who had just staked their claim earlier that spring (1859) near a cottonwood grove and a creek. He begged for work and shelter and they let him sleep in the wagon until winter set in. They didn't have much to pay him, but he managed to earn his keep helping them break the sod and plant crops. He helped them build a larger sod roof dwelling and small pig barn. He also learned a bit more on how to read and write. The mother of the family recorded much of this story well after the fact when he actually married into the family some 5 years later. One would surmise that the young man turned away from gold by the farmer's good-looking young daughter.
The reasoning given for his desire to head west was the opportunity to have a better life and the fact that he had seen death and deprivation where he was so he thought that it couldn't have been worse heading west where some of the "good things" aren't already taken.
From his story and several others that I read doing that research, I drew the general conclusion that heading west for land, gold, cattle, or any other riches/opportunity certainly tended to favor the young, desperate, or unattached looking to escape their present life with the dream of something better. At the time I sort of likened it to heading off to college with the dream of a better life not believing that you could fail out (or change majors/career paths), only with more guns, disease, criminals, and potentially hostile natives. In any case, nearly all of the journals/writings I read seemed to speak to this idea that whatever the odds they were going to have things better going west because they had the freedom to do so and would succeed by force of will. I suspect in many cases these journals were written a bit after the fact and some of the rougher or unsavory bits seemed to be glossed over. The other piece of it is perhaps a survivorship-bias. Another 50-100 miles down the trail and this story might have ended with some bleached bones on the Kansas Prarie.